If a star contains a certain element, it can be determined by studying the star’s

A.Emission Spectrum
B.Corona
C.Sunspot Activity
D.Main Sequence

Using trigonometric functions, we can calculate the plane's distance from Orlando after deviating from the course and the extra distance flown after correcting course back towards Orlando.

To solve the problem regarding the pilot's flight from Miami to Orlando, we will employ trigonometric concepts to determine the distance of the plane from Orlando after flying 100 miles off course and to calculate how much farther the flight would be than a direct route after the course correction.

a) After flying 100 miles at 10 degrees off course, we can use right triangle trigonometry to find the distance from Orlando. We know the adjacent side (100 miles of flight) and the angle (10 degrees); we are interested in finding the hypotenuse, which represents the distance from the starting point, and the opposite side, which will represent the deviation from the direct path towards Orlando. Using the cosine function, cos(10 degrees)=adjacent/hypotenuse=100/hypotenuse, we can solve for the hypotenuse. Then, using the sine function, sin(10 degrees)=opposite/hypotenuse, we can solve for the opposite side, which, when subtracted from the original 220 miles, will give us the remaining distance to Orlando.

b) If the pilot adjusts course after 100 miles, they will now have to fly not directly to Orlando but to the point they have deviated from their path. This forms another right triangle with one known side (the deviation) and another side that is part of the remaining distance towards Orlando. By applying the Pythagorean theorem, we can find the added distance by determining the hypotenuse of this new triangle and comparing it to the direct route that was 220 miles originally.

The plane is approximately 99.67 miles from Orlando after flying 100 miles in a direction 10 degrees off course. If the pilot adjusts the course, the total distance of the flight will be approximately 218.28 miles farther than a direct route.

To determine the distance the plane is from Orlando after flying in a direction 10 degrees off course for 100 miles, we can use trigonometry. Since the plane is 10 degrees off course, we can create a right triangle where the hypotenuse represents the plane's actual distance from Orlando and the adjacent side represents the distance the plane has traveled. Using the cosine function, we can calculate that the plane is approximately 99.67 miles from Orlando.

If the pilot adjusts the course after flying 100 miles, the total distance of the flight will be the sum of the straight-line distance from Miami to Orlando and the additional distance traveled in the adjusted course. To find the additional distance, we can use the Pythagorean theorem to calculate the length of the hypotenuse of a right triangle where one side is the straight-line distance from Miami to Orlando (220 miles) and the other side is the distance the plane has traveled (100 miles). The additional distance will be approximately 218.28 miles.

Final answer:

The force exerted by the rope on the crate is 152.0 N.

Explanation:

To calculate the force exerted by the rope on the crate, we can use Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, the mass of the crate is 40.0 kg and the acceleration is 3.80 m/s². Therefore, the force exerted by the rope on the crate can be calculated as:

Force = mass * acceleration

Force = 40.0 kg * 3.80 m/s²

Force = 152.0 N

Therefore, the force exerted by the rope on the crate is 152.0 N.

Answer:

A or B (mostly A)

Explanation:

After 14 billion years, approximately 85% of the original parent isotope will still exist, compared to roughly 45% of parent isotope C, 12.5% of parent isotope B, and nearly none of the parent isotope A!

We know curve D represents the parent isotope with the longest half-life, and curve A represents the parent isotope with the shortest half-life!

We also know it cannot be D or C. So we are stuck with curves B and A! However, since parent isotope B has 12.5% parent isotopes left after 14 billion years(1billion years before the year we are talking about), and nearly none of the parent isotope A is left, this leads me to beleive that the answer is curve, or parent isotope, A!

I am sorry if i am wrong though.

Have a marvelous day!

Answer: The correct option is C.

Explanation:

Longitudinal wave is a wave in which the particles vibrates parallel to the direction of the energy transportation of the wave .

For example, sound wave.

Sound wave consists of rarefaction and compression. In rarefaction, the density of the particles is more in comparison to compression.

Sound wave needs a medium for its propagation. It can travel in solid, liquid and gas. It cannot travel in vacuum.

Therefore, the true statement about the movement of sound waves is only (C) option.

Answer: pitch

Explanation:

Pitch is the perception of the frequency of a sound: this means that pitch is directly proportional to the frequency of the sound.

Therefore, if the frequency of the sound wave increases, the pitch increases as well.

To find the total time of flight of the artillery shell, we can use the kinematic equation for vertical motion. By calculating the vertical component of the initial velocity and plugging in the known values, we can solve for the time of flight. Finally, we can convert the time to minutes by dividing by 60.

To find the total time of flight of the shell, we can use the kinematic equation for vertical motion: d = v0yt + 0.5gt2. In this equation, d represents the vertical displacement of the shell (which is 200 m), v0y represents the vertical component of the initial velocity (which can be found using v0y = v0sin(θ)), t represents the time of flight, and g represents the acceleration due to gravity.

Since the shell is fired at an angle of 62.7° above the horizontal, the vertical component of the initial velocity can be calculated as v0y = 1520 m/s * sin(62.7°). Plugging in the known values, we can solve for t.

Once we have the time of flight, we can convert it to minutes by dividing by 60 (since there are 60 seconds in a minute).

Answer : [tex]F=5.8\times 10^2\ Newtons[/tex] amount of force is required to push a sofa.

Explanation :

It is given that,

The mass of sofa, m = 59 kg

Acceleration, [tex]a=9.75\ m/s^2[/tex]

According to Newton's second law of motion :

F = ma

m is the mass and a is the acceleration produced.

[tex]F=59\ kg\times 9.75\ m/s^2[/tex]

F = 575.25 Newtons

[tex]F=5.75\times 10^2\ Newtons[/tex]

or

[tex]F=5.8\times 10^2\ Newtons[/tex]

Hence, this is the required solution.

33 60 

--- 

1980 33*60sec = 1980 sec for comparison

By definition, we have to:

[tex] vf = a * t + vo
[/tex]

Where,

vf: final speed

vo: initial speed

t: time

a: acceleration

Clearing the acceleration we have:

[tex] a = \frac{vf-vo}{t}
[/tex]

When replacing values we have to take into account two things:

1) Assume that the given speeds are positive

2) The time must be in seconds

The time in seconds is:

[tex] t = 33 * 60

t = 1980
[/tex]

Then, replacing values we have:

[tex] a =\frac{7.1-2.7}{1980}
[/tex]

[tex] a = 0.002 \frac{m}{s ^ 2}
[/tex]

Answer:

The average acceleration of the treadmill during this period is:

[tex] a = 0.002 \frac{m}{s ^ 2}
[/tex]

ind the velocity my using the conservation of energy mgh=1/2mv^2. At the bottom, the mass is turning in a circle with tension pointing up towards the center of the circle and weight pointing down. Use the centripetal force requirement mv^2/r=T-W and solve for T. Hope this helps.

The speed of the mass at the bottom of its path is approximately 6.51 m/s, and the tension in the string at that point is approximately 141.4 N, which is calculated using the conservation of energy and understanding the forces in a circular motion.

To solve both parts of the problem involving the mass hanging on the end of a massless rope and released from rest, we apply principles of physics, specifically conservation of energy and dynamics of a simple pendulum. Conservation of energy tells us that the potential gravitational energy at the top is converted to kinetic energy at the bottom of its path. The tension in the string at the bottom can be calculated by understanding the forces acting on the mass at that point, which include the centripetal force necessary to maintain its circular path and the gravitational force pulling it downward.

Using conservation of energy, we have:

Potential Energy at top (U): U = mgh = mgL

Kinetic Energy at bottom (K): K = 1/2 m[tex]v^2[/tex]

Setting U equal to K gives us:

mgL = 1/2 m[tex]v^2[/tex]

From which we can solve for v, the speed at the bottom:

v = [tex]\sqrt{2gL}[/tex]

Substituting in the values (g = 9.8 m/[tex]s^2[/tex], L = 2.16 m),

v = [tex]\sqrt{2 \times 9.8 \times 2.16} = \sqrt{42.336} \approx 6.51 m/s[/tex]

The tension in the string (T) at the bottom is the sum of the gravitational force and the centripetal force required to keep the mass moving in a circle:

T = mg + m[tex]v^2[/tex]/L

Substituting in the known values:

T = 4.6 × 9.8 + 4.6 × [tex](6.51)^{2/2.16}[/tex]

T = 45.08 + 4.6 × (42.3961)/2.16

T = 45.08 + 96.3273

T = 141.4073 N

The tension at the bottom of the path is approximately 141.4 N.

The law is C.) Equal areas law

First, we need to calculate the total distance that the diver travelled. The diver jumped off a 10-meter tower and went 5 meters under the water. Therefore, the total distance travelled by the diver is 10 meters (from the tower) plus 5 meters (underwater), which equals 15 meters.

Next, we will determine the work done on the diver. The work done is equal to the change in potential energy, which can be calculated by multiplying the diver's mass by gravity and then by the total distance the diver travelled. Given that the diver's mass is 70kg and the acceleration due to gravity is 9.8m/s², the work done is 70kg * 9.8m/s² * 15m, which equals 10290 Joules.

Finally, we'll find the average resistance force exerted on the diver by the water. The work done on the diver is also equal to the average force times the distance. Therefore, the average force is the work done divided by the distance. When you divide the work done (10290 Joules) by the total distance travelled (15 meters), you get an average force of 686 Newtons.

Hence, the total distance travelled by the diver in water is 5 meters, the work done on the diver is 10290 Joules, and the average resistance force exerted on the diver by the water is 2058 Newtons.

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Final answer:

The necessary condition for conservation of momentum is the absence of net external forces on the system, making it closed or isolated. In this state, the total momentum remains constant, which is fundamental in solving physics problems related to the motion of objects.

Explanation:

The necessary condition for the conservation of momentum is that there should be no net external force acting on the system. In physics, this is known as an isolated system or a closed system. When analyzing problems using the conservation of momentum principle, it is crucial to identify whether the system in question meets this condition. In such a system, the vector sum of all the momenta remains constant. This is because, according to Newton's Second Law, when there is no net external force, there would be no change in the momentum of the system. Even in the presence of internal forces, like during a collision between particles, as long as the net external force is zero, the total momentum before and after an event remains the same.

To apply the conservation of momentum, the first step always involves confirming that you're dealing with a closed system with no net external force. This means even with forces like friction or air resistance, if they are considered external, they must be negligible or balanced out by other forces to maintain conservation of momentum.

Answer: Option (b) is the correct answer.

Explanation:

According to ohm's law, the relationship between voltage, resistance, and current is that current passing through a conductor is directly proportional to the voltage over resistance.

Mathematically,           I = [tex]\frac{V}{R}[/tex]

From this relationship we can see that when we decrease the voltage, and do not change the resistance, the current will also decrease. As current is directly proportional to voltage and inversely proportional to resistance.

Answer:

360

Explanation:

just took the test

Final answer:

To find the spring constant, use the formula for elastic potential energy,[tex]U = 1/2 k x^2[/tex]. Given that U = 16.2 J and x = 0.30 m, the spring constant is calculated to be 360 N/m.

Explanation:

The spring constant, denoted by k, is a measure of the stiffness of a spring. It represents the force required to stretch or compress a spring by a certain amount.

The question asks about finding the spring constant from the given elastic potential energy and displacement.

The formula for elastic potential energy stored in a spring is [tex]U = 1/2 k x^2[/tex], where U is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position. Using this formula and the given values, we can solve for k as follows: [tex]16.2 J = 1/2 k (0.30 m)^2[/tex]. After calculating, we find the spring constant is 360 N/m.

Answer:

Part a)

[tex]v_f = 5.48 m/s[/tex]

Part b)

[tex]v_1 = -2.67 m/s[/tex]

[tex]v_2 = 2.81 m/s[/tex]

Part c)

[tex]h_1 = 0.36 m[/tex]

[tex]h_2 = 0.40 m[/tex]

Explanation:

Part a)

As we know by energy conservation law

initial kinetic energy + initial potential energy = final kinetic energy + final potential energy

So here we know that

[tex]\frac{1}{2}mv_i^2 + mgh_i = \frac{1}{2}mv_f^2 + mgh_f[/tex]

[tex]v_i = 5 m/s[/tex]

[tex]h_i = 0.260 m[/tex]

[tex]h_f = 0[/tex]

now we have

[tex]v_f^2 = v_i^2 + 2gh[/tex]

[tex]v_f^2 = 5^2 + 2(9.8)(0.260)[/tex]

[tex]v_f = 5.48 m/s[/tex]

Part b)

As we know that collision is perfectly elastic collision

so we will have

[tex]m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}[/tex]

[tex]1.55(5.48) + 0 = 1.55 v_1 + 4.50 v_2[/tex]

also we know for elastic collision

[tex]v_2 - v_1 = 5.48[/tex]

[tex]v_1 = -2.67 m/s[/tex]

[tex]v_2 = 2.81 m/s[/tex]

Part c)

Now the height of each ball is given by

[tex]h = \frac{v^2}{2g}[/tex]

[tex]h_1 = \frac{2.67^2}{2(9.81)}[/tex]

[tex]h_1 = 0.36 m[/tex]

[tex]h_2 = \frac{2.81^2}{2(9.81)}[/tex]

[tex]h_2 = 0.40 m[/tex]

The student's question involves applying the conservation of mechanical energy to find the speed of a ball before impact, using the conservation of momentum and kinetic energy for an elastic collision, and determining the height of the swing post-collision in physics.

To solve the student's problem, we will apply the principles of conservation of mechanical energy and conservation of momentum which are fundamental concepts in physics, specifically in the field of mechanics. Given the nature of the questions, this falls into the category of a high school physics problem, typically encountered by students learning about motion and energy.

For part (a), the conservation of mechanical energy states that the total mechanical energy (kinetic plus potential) in an isolated system remains constant if only conservative forces are acting. Initial mechanical energy at the height h will be equal to the kinetic energy just before the impact.

For part (b), an elastic collision is one where both momentum and kinetic energy are conserved. We would apply both the conservation of momentum and kinetic energy equations to find the velocities of the two balls post-collision.

For part (c), after the collision, to find how high each ball swings, we would convert the kinetic energies of the balls just after the collision to potential energies at the peak of their respective swings, assuming no energy is lost to air resistance.

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The baseball hits the ground approximately 75.8 meters from the base of the cliff. This is calculated using physics principles of gravity and projectile motion, considering the height of the cliff, acceleration due to gravity, and the horizontal velocity of the baseball.

This question involves what is called projectile motion, which is a topic in physics. To find the horizontal distance from the base of the cliff where the ball hits the ground, we need to know the time it takes for the ball to fall. Incidentally, the horizontal velocity doesn't affect this; it will take the same amount of time to hit the ground whether it's thrown horizontally or simply dropped.

We know the acceleration due to gravity is 9.8 m/s². The time it takes for the ball to hit the ground can be calculated using the formula: t = √(2h/g), where h is the height and g is the acceleration due to gravity. Substituting 45m for h and 9.8m/s² for g gives: t = √(2*45/9.8) which equals about 3.03 seconds.

In this time, the ball will move horizontally at 25 m/s for 3.03 seconds, a total of about 75.8 meters. So, the ball hits the ground approximately 75.8 meters from the base of the cliff. This is assuming negligible air resistance.

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The correct answer is - a. was a sign of danger.

Once the people saw that the ocean waters are receding and were living vast space without water behind them, they knew that something big and very dangerous will happen. And in fact it did. The water that was sucked in in the place were there was a crack on the ocean floor, got shot back under big pressure and it had very big speed, as well as having waves that were destroying anything on their way.

Answer:

Option (A)

Explanation:

Tsunamis are the series of large waves that are generated in the large water bodies such as seas and oceans, due to an earthquake, underwater explosion or landslide. These waves can rise up to a height of about hundreds of meters.

A receding ocean is a sign of danger that signifies that a tsunami is approaching. During this time the water level drops down unusually along the coastline. It is a kind of warning that is given to the people living in the coastal areas to evacuate it as soon as possible in order to save their lives.

Thus, the correct answer is option (A).

Answer:

The real answer is A. 1

Explanation:

To ensure 100% internal reflection in water, the light must first pass through glass or a diamond before entering the water.

The refractive index of a substance also known as the refraction index or index of refraction is a dimensionless quantity that specifies how quickly light passes through it in optics.

The speed at which light waves travel changes as the medium changes. The absolute refractive index changes.

Angle of incidence must be larger than critical angle for entire internal reflection.

Total internal reflection occurs in water when the refractive index on the other side of the water is lower and the angle of incidence is larger than the critical angle.

So there must be oxygen on the other side of the river. Light must go from a medium object of greater density to a medium object of lower density for total internal reflection to occur.

To ensure 100% internal reflection in water, the light must first pass through glass or a diamond before entering the water.

In the water, the angle of incidence is 50 degrees. It experiences entire internal reflection because the angle of incidence is larger than the air-water critical angle of roughly 48°.

To learn more about the index of refraction refer to the link;

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