A riverboat took 2 h to travel 24km down a river with the current and 3 h to make the return trip against the current. Find the speed of the boat in still water and the speed of the current.

Answer:

d) g/2

Explanation:

We need to use one of Newton's equations of motion to find the position of the stone at any time t.

x(t) = x₀(t) + ut - ¹/₂at²

Where

x₀(t) = initial position of the stone.

x(t) - x₀(t) = distance traveled by the stone at any time.

u = initial velocity of the stone

a = acceleration of the stone

t = time taken

On both planets, before the stone was thrown by the astronaut, x = 0 and t = 0.

=> 0 = x₀(t)

=> x₀(t) = 0

On earth, when the stone returns into the hand of the astronaut at time T on earth, x = 0.

=> 0 = 0 + uT - ¹/₂gT² (a = g)

=> uT = ¹/₂gT²

=> g = 2u/T

On planet X, when the stone returns into the hand of the astronaut, time = 2T , x = 0.

=> 0 = 0 + u(2T) - ¹/₂a(2T)²

=> 2uT = 2aT²

=> a = u/T

By comparing we see that a = g/2.

Final answer:

The acceleration due to gravity on planet X is determined by comparing the time it takes for a stone thrown vertically upward to return to the thrower's hand. Using kinematic equations and given that it takes twice the time to return on planet X as it does on Earth, we deduce the acceleration on planet X is half that of Earth's gravity (g/2).

Explanation:

The question concerns finding the acceleration due to gravity on an unknown planet, which is an essential concept in physics. To determine the gravitational acceleration (g) on planet X, given that a stone thrown with the same initial upward velocity as on Earth returns in 2T instead of T, we can use the kinematic equations for motion under constant acceleration.

On Earth, the total time for the stone to return to the thrower's hand is T, which implies that the time to reach the maximum height is T/2. Applying the equation v = u + at, where v is the final velocity (0 m/s at maximum height), u is the initial upward velocity, a is the acceleration due to gravity (which is -g on Earth), and t is the time (T/2), we have 0 = u - g(T/2). Solving for u gives us u = g(T/2).

On Planet X, the total time for the stone to return to the thrower's hand is 2T, so the time to reach maximum height is T. Using the same equation with the acceleration on Planet X as aX, we get 0 = u - aX(T). Since u = g(T/2), we have g(T/2) = aX(T), leading to aX = g/2.

Therefore, the correct answer is (d) g/2.

Final answer:

To reach a child being carried by a river current, the rescue boat, with a speed of 7.30 m/s versus water, must aim at a specific angle upstream accounting for the current's speed of 2.20 m/s. The calculation involves vector addition and trigonometry to counteract the current and ensure a direct path to the child.

Explanation:

The question involves calculating the angle at which a rescue boat must travel to reach a child being carried away by a river current. The river flows at a speed of 2.20 m/s, while the boat's speed in still water is 7.30 m/s. Given the distances from the shore to the child (500 m) and from the boat dock upstream to the child (1100 m), we need to determine the angle relative to the shore for the boat to make a direct rescue.

To solve this, we need to use the concept of vector addition, where the boat's velocity vector and the river's current vector combine to create a resultant vector that points directly to the child's location. The angle can be calculated using trigonometry, particularly the tangent function. However, since the specific calculations and steps to obtain the angle are not provided in the question or the previous examples, it is crucial to understand the principles of vectors and relative motion to approach this problem.

Essentially, the rescue team needs to aim the boat at an angle upstream to counteract the river's flow. The effect of the river's current will adjust the boat's path towards the child. It's a classic application of relative motion in two dimensions, requiring careful consideration of both the magnitude and direction of the vectors involved.

Final answer:

Dispersion refers to the spreading of a signal where different parts of the signal reach the recipient at varying times, affecting the wave by causing signal broadening due to the speed differential of its frequency components.

Explanation:

The term that refers to the spreading of a signal where different parts arrive at the receiver at different times is known as dispersion. Dispersion affects waves by causing a broadening of the signal, as different frequency components of the wave travel at different speeds. This is especially important in optical fibers, where dispersion can cause pulse broadening, potentially limiting the bandwidth and impairing the integrity of the data being transmitted. Option C is correct .

Factors such as scattering and refraction directly relate to the phenomenon of dispersion. For instance, scattering causes the redirection of light within a medium and refraction is the bending of a wave when it enters a medium where its speed is different. In the context of signal transmission, residence time is the average time a molecule spends in its reservoir, though this concept is less directly related to the question at hand.

Answer: 2.82m/s

Explanation:

Wave speed(v) is the product of the frequency (f) of a wave and its wavelength (¶)

V = f¶

Since wavelength is the distance between two successive crests or trough, the wavelength given is 1.40m i.e ¶ = 1.40m

If the total crest is 25, this means that 25 oscillations occurs in 12.4s.

Since the number of oscillation made in one second is the frequency, frequency = 25/12.4 = 2.01cycle/seconds

Speed of the wave v = 2.01×1.4

V =

Wave speed is 2.82m/s

Answer

From the question we can see that the in medium  1 speed of light is 200,000 Km/s where as in Medium 2 speed of light is 250,000 km/s.

We can conclude that medium 1 is denser than Medium 2.

In third medium Light speed halts so, the third medium is opaque.

We can say that

Medium 1 can be either water, glass.

Medium 2 will be gas

Medium 3 will be an opaque material.

Answer:

D

Explanation:

Answer:

The stuntman will not make it

Explanation:

At the bottom of the swing, the equation of the forces acting on the stuntman is:

[tex]T-mg = m\frac{v^2}{r}[/tex]

where:

T is the tension in the rope (upward)

mg is the weight of the man (downward), where

m = 82.5 kg is his mass

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

[tex]m\frac{v^2}{r}[/tex] is the centripetal force, where

v = 8.65 m/s is the speed of the man

r = 12.0 m is the radius of the circule (the length of the rope)

Solving for T, we find the tension in the rope:

[tex]T=mg+m\frac{v^2}{r}=(82.5)(9.8)+(82.5)\frac{8.65^2}{12.0}=1322 N[/tex]

Since the rope's breaking strength is 1000 N, the stuntman will not make it.

I believe the answer would be D

The gravitational force is weaker and can only attract objects but the electrostatic force is strong and can both attract and repel. - This is the most completely describes the differences between the gravitational force and the electrostatic force.

The main differences are:

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The current across R1 in circuit A is the same as the current across the resistors in circuit B.

In circuit A, two resistors R1 and R2 are connected in series. In circuit B, two identical resistors are connected in parallel. In a series circuit, the current is the same in each resistor. Therefore, the current across R1 in circuit A is the same as the current across the resistors in circuit B, since they are connected in parallel.

Answer:

There are finally 4 rotations per second.

Explanation:

If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was. We need to find the final angular velocity. It is a case of conservation of angular momentum such that :

[tex]I_1\omega_1=I_2\omega_2[/tex]

Let [tex]I_1=I[/tex] , [tex]I_2=\dfrac{I}{4}[/tex] and [tex]\omega_1=1[/tex]

So,

[tex]\omega_2=\dfrac{I_1\omega_1}{I_2}[/tex]

[tex]\omega_2=\dfrac{I\times 1}{(I/4)}[/tex]

[tex]\omega_2=4\ rev/sec[/tex]

So, there are finally 4 rotations per second. Hence, this is the required solution.

Final answer:

When a trapeze artist reduces their rotational inertia to one fourth while rotating, their rotational speed increases to four times its original rate to conserve angular momentum, resulting in 4 rotations per second.

Explanation:

The question pertains to the conservation of angular momentum, which is a principle in physics stating that if no external torque acts on an object, the total angular momentum will remain constant. For a trapeze artist or any rotating body, if the moment of inertia decreases, the rotational speed (number of rotations per second) must increase proportionally to conserve angular momentum.

If a trapeze artist is rotating once each second and contracts to reduce the rotational inertia to one fourth, her rotational speed must increase to four times what it was to conserve angular momentum. Therefore, the new rotation rate will be 4 rotations per second.

Answer:

Explanation:

Given

Voltage [tex]V=16\ V[/tex]

Work done [tex]W=1705\ J[/tex]

Work is Equivalent to energy

We know that Charge is given by

[tex]Q=I\cdot t[/tex]

where I=current

t=time

Energy [tex]E=P\times t[/tex]

P=power

P=V\times I

V=Voltage

I=current

Also Energy [tex]E=V\cdot I\cdot t[/tex]

[tex]I=\frac{E}{V\cdot t}[/tex]

Substitute the value of I in charge

[tex]Q=\frac{E}{V\cdot t}\times t[/tex]

[tex]Q=\frac{E}{V}[/tex]

[tex]Q=\frac{1705}{16}[/tex]

[tex]Q=106.56\ C[/tex]        

Answer:

Time, t = 2.80seconds

Explanation:

Calculating net Torque, T

Torque(net)= F2(0.08m) - F1(0.03)

Torque(net) = (27×0.08)-(12×0.03)

Torque(net)= 2.16 - 0.36 =1.8N/m

Pi/4= Torque(net)/ Inertia

3.142/4= 1.8/9 = 0.2rad/s^2=a

Pi/4= 1/2 at^2

3.142/4=1/2×0.2 ×t^2

0.7855= 0.1 t^2

t = sqrt(0.7856/0.1)

t= sqrt(7.855)

t=2.80 seconds

By Assuming that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. then the time in seconds is 2.80seconds

Force can be denoted as the parameter obtained by  pushing or pulling of any object which result in object’s interaction or movement, without force the objects can not move, it can be stopped or change the direction.

Force is a  quantitative property and it is an  interaction between two physical bodies, means an object and its environment, there are different types of forces in nature.

If an object is in its moving state then it will be either static or motion,  if it is pushed or pulled the object will change its position and The external push or pull upon the object called as Force.

There are two types of forces such as contact force which are the force occurs when we apply some effort on the object such as Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force

Non-Contact forces can be defined as  the force occur from a distance  such as Electromagnetic Force, Gravitational Force, Nuclear Force

Calculating net Torque, T, Torque(net)= F2(0.08m) - F1(0.03)

Torque(net) = (27×0.08)-(12×0.03)

Torque(net)= 2.16 - 0.36 =1.8N/m

Pi/4= Torque(net)/ Inertia

3.142/4= 1.8/9 = 0.2rad/s^2=a

Pi/4= 1/2 at^2

3.142/4=1/2×0.2 ×t^2

0.7855= 0.1 t^2

t = sqrt(0.7856/0.1)

t= sqrt(7.855)

t=2.80 seconds

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Answer:

Potential difference will be equal to 2156.25 volt

Explanation:

We have given kinetic energy of electron [tex]KE=3.45\times 10^{-16}J[/tex]

Charge on electron [tex]e=1.6\times 10^{-19}C[/tex]

Let the potential difference is V

So energy electron will be equal to [tex]E=qV[/tex], here q is charge on electron and V is potential difference

This energy will be equal to kinetic energy of the electron

So [tex]1.6\times 10^{-19}\times V=3.45\times 10^{-16}[/tex]

V = 2156.25 volt

So potential difference will be equal to 2156.25 volt

Answer:

a= - 4.2 m/s².

Explanation:

Given that

u = 22 m/s

v= 4.9 m/s

t= 4 s

The average acceleration = a

We know v = u +at

v=final velocity

u=initial velocity

Now by putting the values in the above equation

4.9= 22 + a x 4

[tex]a=\dfrac{4.9-22}{4}\ m/s^2[/tex]

a= - 4.2 m/s².

Therefore the acceleration will be - 4.2 m/s².

a= - 4.2 m/s².

Negative indicates that velocity and acceleration is is opposite direction.

Answer : The number of half-life periods will be, 3

Explanation :  Given,

Initial amount of lead = 10 kg

Amount of lead after decay = 1.25 kg

Half-life = 22 years

Formula used :

[tex]a=\frac{a_o}{2^n}[/tex]

where,

a = amount of reactant left after n-half lives

[tex]a_o[/tex] = Initial amount of the reactant

n = number of half lives

[tex]t_{1/2}[/tex] = half-life

Now put all the given values in the above formula, we get:

[tex]1.25=\frac{10}{2^n}[/tex]

[tex]2^n=8[/tex]

[tex]2^n=2^3[/tex]

[tex]n=3[/tex]

Thus, the number of half-life periods will be, 3

Answer:

Explanation:

We have equation of motion v = u + at

     Initial velocity, u = 20 m/s

     Final velocity, v = 0 m/s    

Case 1:-

     Time, t = 24 s

     Substituting

                      v = u + at  

                      0 = 20 + a x 24

                      a = -0.8333 m/s²

     Force = Mass x Acceleration = 6110 x -0.8333 = -5092 N

     Force exerted is 5092 N towards opposite direction of motion of bus.

Case 2:-

     Time, t = 3.90 s

     Substituting

                      v = u + at  

                      0 = 20 + a x 3.90

                      a = -5.13 m/s²

     Force = Mass x Acceleration = 6110 x -5.13 = -31333 N

     Force exerted is 31333 N towards opposite direction of motion of bus.

The average force exerted on the bus with gentle braking is approximately -5092 N, and with slamming the brakes, it is approximately -31342 N. Negative values indicate the force direction is opposite to the motion.

To calculate the average force exerted on the bus during both stops, we will use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by the acceleration (F = ma). Here, the acceleration can be calculated using the formula for deceleration since the bus is coming to a stop:

Now, we can calculate the average force (F) exerted in both cases by multiplying the mass of the bus (m = 6110 kg) by the deceleration (a).

Since the bus is stopping, the negative sign indicates the direction of the force is opposite to the initial direction of motion.

Answer:

Just maintain the course you are on and your speed.

Explanation:

When you see a green and a white light, then from the port (left) side you will start coming across another craft. You are the stand-alone craft in this scenario and therefore should stay consistent with your pace and direction. The other craft must take important and early measures to keep the craft away from you.

Answer:

0.8m/s

Explanation:

Weight of mas,F=763 N

Mass of man=[tex]\frac{F}{g}=\frac{763}{9.8}=77.86 kg[/tex]

By using [tex]g=9.8m/s^2[/tex]

Weight of flatcar=F'=3513 N

Mass of flatcar=[tex]\frac{3513}{9.8}=358.5 Kg[/tex]

Total mass of the system=Mass of man+mass of flatcar=77.86+358.5=436.36 kg

Velocity of system=19.8m/s

Let v be the velocity of flatcar with respect to ground

Velocity of man relative to the flatcar=[tex]-4.68m/s[/tex]

Final velocity of man with respect to ground=v-4.68

By using law of conservation of momentum

Initial momentum=Momentum of car+momentum of flatcar

[tex]436.36(19.8)=77.86(v-4.68)+358.5v[/tex]

[tex]8639.928=77.86v-364.3848+358.5v[/tex]

[tex]8639.928+364.3848=436.36 v[/tex]

[tex]9004.3128=436.36v[/tex]

[tex]v=\frac{9004.3128}{436.36}[/tex]

[tex]v=20.6 m/s[/tex]

Initial speed of flatcar=Speed of system

Increase in speed=Final speed-initial speed=20.6-19.8=0.8m/s

Answer:

The tangential speed of a point on the "equator" of the baseball is 4.33 m/s.

Explanation:

Given that,

Linear speed of base ball = 42.5 m/s

Distance = 16.0 m

Angle = 44.5 rad

Radius of baseball = 3.67 cm

We need to calculate the flight time

Using formula of time

[tex]t=\dfrac{d}{v}[/tex]

Put the value into the formula

[tex]t=\dfrac{16.0}{42.5}[/tex]

[tex]t=0.376\ sec[/tex]

We need to calculate the number of rotation

Using formula of number of rotation

[tex]n=\theta\time 2\pi[/tex]

[tex]n=\dfrac{44.5}{2\pi}[/tex]

[tex]n=7.08[/tex]

We need to calculate the time for one rotation

Using formula of time

[tex]T=\dfrac{t}{n}[/tex]

Put the value into the formula

[tex]T=\dfrac{0.376}{7.08}[/tex]

[tex]T=0.053\ sec[/tex]

We need to calculate the circumference

Using formula of circumference

[tex]C=2\pi\times r[/tex]

Put the value into the formula

[tex]C=2\pi\times3.67\times10^{-2}[/tex]

[tex]C=0.23\ m[/tex]

The tangential speed is equal to the circumference divided by the time. it takes to complete one rotation.

We need to calculate the tangential speed

Using formula of tangential speed

[tex]v=\dfrac{C}{T}[/tex]

Put the value into the formula

[tex]v=\dfrac{0.23}{0.053}[/tex]

[tex]v=4.33\ m/s[/tex]

Hence, The tangential speed of a point on the "equator" of the baseball is 4.33 m/s.

Answer:

The earth is considered to be a closed system, where the concentration of rocks, metals, C, N, O and H₂O on earth remains constant.

So, it is essential that the biogeochemical cycle renews these materials while moving through the earth subsystems.

Explanation:

The biogeochemical cycle is usually defined as the circulation of chemical components such as Carbon, Nitrogen, Phosphorous, Oxygen, rocks, and metals within the different spheres and interaction of biotic and non-biotic factors.

These components are continuously in motion from one sphere to another. For example, the organism takes up the elements through food and some of these components such as carbon is released into the atmosphere in the form of CO₂. After the death of the organisms, the decomposers feed on these elements, where some of it is consumed by them and the remaining is eliminated into the atmosphere.

So, this is how the elements are renewed, and they are conserved. The total concentration of these elements remains constant considering the earth to be a closed system.

Thus, the correct answers are given above.

Answer:

remains constant and renews

Explanation:

Answer:

option A

Explanation:

given,

distance of the moon 1 from planet = 0.7 AU

Time period of moon 1 = 27.8 earth days

distance of the moon 2 from the planet = 1.2 AU

time period of the moon 2 = ?

using Kepler's formula

[tex]T^2 = \dfrac{4\pi^2}{GM}\ R^3[/tex]

now,

only variable in the formula is time period and distance.

so,

[tex]\dfrac{T_2^2}{T_1^2}=\dfrac{R_2^3}{R_1^3}[/tex]

[tex]\dfrac{T_2^2}{27.8^2}=\dfrac{1.2^3}{0.7^3}[/tex]

  T₂² = 3893.49

  T₂ = 62.3 earth days

Hence, the correct answer is option A

Answer:A) This is most appropriate for an output measure of capacity.

Explanation: Toothpaste is a paste used to promote oral health and hygiene, Most toothpaste contain an active agent(floride) and it acts as an abrasive agent which helps to remove dental plaques or unwanted attachments to the teeth.

Among the options the Option(A) which says that THIS IS MOST APPROPRIATE FOR THE MEASURE OF CAPACITY is the statement that best Describes the situation. Toothpastes have a long history as it can be traced to about 4000years ago.

Answer:

To me it would only make sense for it to be 51.33

Explanation:

w≈51.33

Length  3

Area  154

The width of the outside of the picture frame is 11 cm.

The distinction between a figure's length and width is that length denotes a figure's longer side, while width denotes its shorter side.

Given

L = w + 3

L w = 154

(w+3)w = 154

w² + 3 w - 154 = 0

(w+14)(w-11) = 0

w = 11 cm

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Force is derived from the equation F = ma, resulting in units of Newtons (N). For a 10-ton truck decelerating over 1 second from 55 mph, we convert mass to kg and speed to m/s to calculate force, likely resulting in a force measured in kilonewtons (kN) or meganewtons (MN) due to the large mass and deceleration involved.

The subject of this question is how to derive a unit for force starting with SI base units, and finding a convenient unit for the force resulting from a specific collision scenario. Starting from the base, force (F) can be defined using Newton's second law, F = ma (force equals mass times acceleration), where mass has units of kilograms (kg), and acceleration is measured in meters per second squared (m/s²). Thus, the unit of force in the SI system is the Newton (N), defined as the force needed to accelerate a 1-kg object by 1 m/s².

To find a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 miles per hour and assuming a 1 second deceleration time, we first convert the truck's mass to kilograms (10 tons = 9,071.85 kg, assuming 1 ton = 907.185 kg) and its speed to meters per second (55 mph ≈ 24.5872 m/s, assuming 1 mile = 1.60934 km and 1 hour = 3600 seconds). The deceleration rate (a) can be calculated assuming the final velocity (v) is zero and the time (τ) is 1 second, giving us a = -24.5872 m/s² (negative sign denotes deceleration). Thus, applying F = ma, the force of the collision can be calculated, and due to the large numbers involved, units such as kilonewtons (kN) or meganewtons (MN) may be more convenient depending on the exact outcome of the calculation.

The force resulting from the collision with a 10-ton trailer truck moving at 55 miles per hour is approximately 245.87 kN.

Starting with the equation for force, F = ma, where:

- F represents force,

- m represents mass,

- a represents acceleration.

In the International System of Units (SI), the base units are:

- Mass ( m ) is measured in kilograms (kg).

- Acceleration ( a ) is measured in meters per second squared [tex](\( \mathrm{m/s^2} \)).[/tex]

Therefore, the unit of force ( F ) in the SI system is:

[tex]\[ \mathrm{kg \cdot m/s^2} \][/tex]

This unit is commonly known as the Newton (N).

Now, let's calculate the force resulting from a collision with a 10-ton trailer truck moving at 55 miles per hour with a deceleration time of 1 second.

First, we need to convert the mass of the trailer truck from tons to kilograms:

[tex]\[ 1 \text{ ton} = 1000 \text{ kg} \][/tex]

So, [tex]\( 10 \text{ tons} = 10,000 \text{ kg} \).[/tex]

Next, let's convert the speed from miles per hour to meters per second:

[tex]\[ 1 \text{ mile} = 1609.34 \text{ meters} \][/tex]

[tex]\[ 1 \text{ hour} = 3600 \text{ seconds} \][/tex]

So, [tex]\( 55 \text{ miles per hour} \)[/tex] is equivalent to:

[tex]\[ \frac{55 \times 1609.34}{3600} \text{ meters per second} \approx 24.587 \text{ m/s} \][/tex]

Given that deceleration time ( t ) is [tex]\( 1 \text{ second} \)[/tex], we can use the formula for acceleration:

[tex]\[ a = \frac{v}{t} \][/tex]

where v is the change in velocity.

Since the truck is decelerating, the change in velocity is from [tex]\( 24.587 \text{ m/s} \) to \( 0 \text{ m/s} \).[/tex]

[tex]\[ a = \frac{0 - 24.587}{1} \text{ m/s}^2 = -24.587 \text{ m/s}^2 \][/tex]

Now, we can calculate the force:

[tex]\[ F = m \times a = 10,000 \text{ kg} \times (-24.587 \text{ m/s}^2) \][/tex]

[tex]\[ F \approx -245,870 \text{ N} \][/tex]

Since force is a vector quantity and its direction is opposite to the direction of motion, the negative sign indicates that the force is acting in the opposite direction of the truck's motion.

For convenience, we can express this force in kilonewtons ( kN ):

[tex]\[ -245,870 \text{ N} = -245.87 \text{ kN} \][/tex]

So, the suggested convenient unit for the force resulting from the collision is [tex]$\mathrm{kN}$[/tex].

Complete Question:

Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes suggest a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 miles per hour. (Assume 1 second deceleration time)

a. MN

b. GN

c. mN

d. kN

e. TN

Answer:

Explanation:

Given

Speed of Henrietta is [tex]v=2.95\ m/s[/tex]

Height of tower [tex]h=39.6\ m[/tex]

Bruce throws the bangle after 7.5 s

During 7.5 s Henrietta travels

[tex]x=2.95\times 7.5=22.125\ m[/tex]

Suppose bangle hit the ground after t sec so bangle will has to cover a distance of x and distance traveled by Henrietta during this time t

Range of bangle when thrown with speed u

[tex]R=u\times t[/tex]

[tex]R=x+2.95\times t-----1[/tex]

bangle will also cover a vertical distance of 39.6 m

so using equation of motion

[tex]h=u_yt+\frac{1}{2}gt^2[/tex]

here initial vertical velocity is zero

[tex]39.6=0+\frac{1}{2}\cdot 9.81\cdot t^2[/tex]

[tex]t=\sqrt{8.0816}[/tex]

[tex]t=2.84\ s[/tex]

Substitute the value of t in  

[tex]u\times 2.84=22.125+2.95\times 2.84[/tex]

[tex]u=10.743\ m/s[/tex]

Explanation:

Mechanical energy (the sum of potential and kinetic energy) is constant:

ME = PE + KE

ME = PE + ½ mv²

PE = ME − ½ mv²

So the slope of the line is -½ of the mass.

In a gravitational potential energy vs velocity^2 graph, the slope symbolizes the mass of the object. The graph represents the conversion of energies - kinetic and gravitational throughout a motion course. Peaks correspond to max potential energy and min kinetic energy, and vice-versa.

The slope of the gravitational potential energy vs the square of the velocity graph represents the object's mass in specific physical circumstances. This is because the equation for kinetic energy (which this graph is showing an indirect relationship with) is (1/2)mv^2, where m is mass and v is velocity. The slope can be interpreted as mass due to the rearrangement of this formula into the form used for this graph (Potential energy = 1/2 * m * v^2), wherein the slope (m) symbolizes the mass of the object.

Moreover, the information encapsulated in the potential energy graph as a whole represents energy conversion from kinetic to gravitational and vice versa. At the peak of a slope/motion course, potential energy is at its maximum and kinetic energy at its minimum. The opposite occurs at the bottom of the slope: both kinetic energy and potential energy reach their minimum values.

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Answer:

Swim in a strong north easterly direction so the the river carries him right across

Explanation:

The swimmer is on the west river bank with intentions of reaching the east river bank directly across him. If he just swims towards the east, the current of the river will carry him downstream landing him in a south easterly position, below where he intended to go. So the right thing to do would be to swim in a strong north easterly direction so the the river carries him right across.

To reach directly across the river from the west bank, the swimmer should head northeast to counteract the southward current of the river. This balancing act of velocities ensures they reach their desired location.

This question deals with the concept of Relative Velocity in Physics. When a swimmer attempts to cross a river, they must take into account the current of the river pushing them downstream. The velocity of the swimmer relative to the water needs to be added to the velocity of the river to get the resultant velocity, which describes the direction the swimmer actually travels relative to the shore.

In this scenario, if the current of the river is flowing due south, the swimmer on the west bank should not aim directly for the point across the river. They should aim slightly upstream to the north to counteract the force of the current. Hence, the swimmer should head in a northeasterly direction, which when combined with the river current, will get them directly across to the eastern shore.

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Answer:

speed of the bicycle = 2.81 m/s

Explanation:

given data

tuning fork rated f = 488 Hz

beat frequency fb = 8 Hz

speed of sound vs = 343 m/s

solution

we get here frequency that rider is listening that is

rider hearing frequency = 488 Hz + 8 Hz

rider hearing frequency = 496 Hz

and when it bouncing from sheer wall at frequency of related to stationary object

frequency = 488 Hz + 4 Hz

frequency =  492 Hz

so now we get speed of the bicycle that is

speed of the bicycle =  (  [tex]\frac{492}{488}[/tex] × 343 )  - 343 Hz

speed of the bicycle = 2.81 m/s

The speed of the bicycle is 2.81 m/s.

Based on the given information,

• The tuning fork rated at frequency (f) 488 Hz.

• The beat frequency (fb) given is 8Hz.  

• The speed of the sound is 343 m/s.  

Now with the help of the given information, the rider is hearing a frequency of,

[tex]=(f+fb)\\=(488+8)\\=496 Hz[/tex]

However, it is bounding from sheer wall at the frequency of,

[tex]=(488+\frac{8}{2})\\= 492 Hz[/tex]

Now the speed of the bicycle will be,

[tex]=(\frac{492}{488} * 343)-343\\=2.811 m/s\\= 2.81 m/s[/tex]

Thus, the speed of the bicycle is 2.81 m/s.

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Answer:

a) speed of belt = 0.8114m/s

b) time required = 0.02secs

c) distance traveled = 0.016m

Explanation:

The detailed and step by step calculation is as shown in the attached files.

Explanation:

There is no any direct relationship between the frequency of a sound relative the intensity of the sound.

Frequency is a perception of pitch of the sound whereas intensity determines the loudness of the sound. Intensity is proportional to amplitude of the sound.

[tex]\beta= log_{10}\frac{I}{I_o}[/tex]

So, it would be hard to determine how much more intense is a 6000 Hz tone than a 80 Hz tone.

Complete answer

A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration of 0.100rad/s2. After making 2844 revolutions, its angular speed is 140rad/s

(a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

Answer:

a) 126.59 radians per second

b) 134.1 seconds

Explanation:

We can use the rotational kinematic equations for constant angular acceleration.

a) For a) let’s use:

[tex]\omega^{2}=\omega_{0}^{2}+2\alpha\varDelta\theta [/tex] (1)

with [tex] \omega_{0}[/tex] the initial angular velocity, [tex] \omega[/tex] the final angular velocity, [tex] \alpha[/tex] the angular acceleration and [tex] \Delta \theta [/tex]the revolutions on radians (2844 revolutions = 17869.38 radians). Solving (1) for initial velocity:

[tex]\sqrt{\omega^{2}-2\alpha\varDelta\theta}=\omega_{0} [/tex]

[tex]\omega_{0}^2=\sqrt{(140)^2 -(2)(0.100)(17869.38)=126.59 \frac{rad}{s}}[/tex]

b) Knowing those values, we can use now the kinematic equation

[tex] \omega=\omega_{0}+\alpha t[/tex]

with t the time, solving for t:

[tex]t=\frac{\omega-\omega_0}{\alpha}=\frac{140-126.59}{0.1} [/tex]

[tex] t=134.1 s[/tex]