a fisherman hooks a trout and reels in his line at speed of 4 inches/second. assume tip of fishing rod is 12 ft above the water directly above the fisherman and the fish is pulled horizontally directly towards the fisherman. Find the horizontal speed of the fish when it is 20 ft from the fisherman. ...?
Answers
Differentiating w.r.t. we obtain dh/dt = (-240/x^2)*dx/dt --> dx/dt = [(x^2)/240]*dh/dt
At x = 20, dh/dt = 4 --> dx/dt = (-400/240)*4 = 20/3
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Answer:
v = 4.66 inch/s
Explanation:
As we know that the height of the rod and the distance from the fisherman is related to each other as
[tex]x^2 + y^2 = L^2[/tex]
now differentiate it with respect to time
[tex]2x\frac{dx}{dt} + 0 = 2L\frac{dL}{dt}[/tex]
here we know that
[tex]\frac{dL}{dt} = 4 inch/s[/tex]
now when
x = 20 ft and y = 12 ft then the length of the line is given as
[tex]L^2 = 12^2 + 20^2[/tex]
[tex]L = 23.3 ft[/tex]
now from above relation
[tex]\frac{dx}{dt} = \frac{L}{x}(\frac{dL}{dt})[/tex]
now we have
[tex]v_x = \frac{23.3}{20} (4 inch/s)[/tex]
[tex]v_x = 4.66 inch/s[/tex]
Related Questions
What is the torque about the center of the sun due to the gravitational force of attraction of the sun on the planet?
Answers
Final answer:
The torque about the center of the Sun due to the Sun's gravitational force on a planet is effectively zero, as the force provides centripetal force for the planet's orbit, not rotational force.
Explanation:
The question asked relates to the field of Classical Mechanics within Physics, particularly regarding the calculation of torque due to gravitational forces. In classical mechanics, torque is the measure of the force that can cause an object to rotate about an axis. The torque (τ) can be calculated by the cross product of the radius vector (r) from the axis of rotation to the point of force application and the force vector (F), τ = r x F. However, in the context of a planet orbiting the Sun, the force of gravity provides centripetal force causing the planet to move in a circular path and does not contribute to the planet spinning or rotating about its own axis. Therefore, the torque about the center of the Sun due to the Sun's gravitational force on a planet is effectively zero.
A football is kicked at an 50 degree angle to the horizontal , travels a horizontal distance of 20m before hitting the ground. what is the initial speed?
Answers
Answer:
Initial speed of football=14.11m/s
Explanation:
Range is the horizontal distance travelled. Therefore using formular for Range,R to determine the speed.
R=V^2Sin2theta/g
Given: R=20m
Theta=50°
20= V^2 Sin(2×50)°/ 9.8
Cross multiply
20×9.8 = V^2 Sin100°
196= V^2×0.9848
V=Sqrt(196/0.9848)
V= 14.11m/s
Suppose a planet has twice the mass of the earth and twice the earth's radius. What is the acceleration of an object in free fall on this planet?
2.5 m/s2
4.9 m/s2
9.8 m/s2
4.9 × 106 m/s2
...?
Answers
The acceleration of an object in free fall on a planet that has twice the mass of the Earth and twice the Earth's radius is 4.9 m/s², half of the acceleration on Earth.
Explanation:The acceleration of an object in free fall on a planet depends on the mass and radius of the planet. In this case, the planet has twice the mass of the Earth and twice the Earth's radius. To calculate the acceleration, we can use the formula for gravitational acceleration:
g = (G * M) / R^2
Where g is the acceleration, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Since the planet has twice the mass and twice the radius of the Earth, we can substitute those values into the formula:
g = (G * 2M) / (2R)^2 = (2 * G * M) / (4 * R^2) = G * M / (2 * R^2)
So the acceleration of an object in free fall on this planet is half of the acceleration on Earth, which is 4.9 m/s².
Geothermal energy is generated by the sun.
True
False ...?
Answers
Q1. After three half-lives of an isotope, 1 billion of the original isotope's atoms still remain in a certain amount of this element. How many atoms of the daughter product would you expect to be present?
Q2. By measuring the amounts of parent isotope and daughter product in the minerals contained in a rock, and by knowing the half-life of the parent isotope, a geologist can calculate the absolute age of the rock. A rock contains 125 g of a radioisotope with a half-life of 150 000 years and 875 g of its daughter product. How old is the rock according to the radiometric dating method?
Answers
The asker of the second question needs a tutorial in radiometric dating. There is little likelihood that the daughter isotope has the same atomic weight as the parent isotope. To measure the mass isotopes doesn't tell us how many atoms of each exist. To get around that let's pretend — which will likely serve the purpose ineptly intended — that the values give an the particle ratio, 125:875.
The original parent isotope count was 125 + 875 = 1000. The remaining parent isotope is 125/1000 or 1/8. 1/8 = (1/2)^h, where h is the number of half-lives.
h = log (1/8) ÷ log(1/2) = 3
And 3 half-lives • 150,000 years/half-life = 450,000 years.
A 17,000-kg airplane lands with a speed of 82 m/s on a stationary aircraft carrier deck that is 115 m long. find the work done by nonconservative forces in stopping the plane
Answers
The work done by nonconservative forces in stopping the 17,000-kilogram airplane landing at a speed of 82 m/s is 57,062,000 Joules. This is calculated by the change in kinetic energy of the airplane when it lands and comes to a stop.
Explanation:The question refers to the concept of work-energy theorem in Physics, especially involving non-conservative forces. The airplane is initially moving and finally comes to rest. Its initial kinetic energy (KE) gets transferred to work done by nonconservative forces, which in this scenario includes friction due to the aircraft carrier deck and air resistance.
The initial kinetic energy of the plane is calculated using the formula 1/2 * m * v^2 where 'm' is the mass of the plane and 'v' is its speed. So, the initial kinetic energy of the plane is 1/2 * 17,000 kg * (82 m/s)^2 = 57,062,000 Joules. When the plane comes to rest, its final kinetic energy is 0. As per the work-energy theorem, the work done by nonconservative forces is equal to the change in the kinetic energy. Therefore, the work done by nonconservative forces in stopping the plane = Initial KE - Final KE = 57,062,000 Joules - 0 = 57,062,000 Joules.
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The work done by nonconservative forces in stopping the airplane is [tex]{57,154,000 \, \text{J}}[/tex].
To find the work done by nonconservative forces (like friction and air resistance) in stopping the airplane, we can use the work-energy principle. The work done by the nonconservative forces is equal to the change in the kinetic energy of the airplane.
Step-by-Step Solution
1. Calculate the initial kinetic energy ([tex]KE_{\text{initial}}[/tex]):
[tex]KE_{\text{initial}} = \frac{1}{2} m v^2[/tex]
where:
- m is the mass of the airplane (17,000 kg),
- v is the initial speed (82 m/s).
[tex]KE_{\text{initial}} = \frac{1}{2} \times 17,000 \, \text{kg} \times (82 \, \text{m/s})^2 \\\\KE_{\text{initial}} = \frac{1}{2} \times 17,000 \times 6,724 \\\\KE_{\text{initial}} = 57,154,000 \, \text{J}[/tex]
2. Calculate the final kinetic energy ([tex]KE_{\text{final}}[/tex]):
Since the airplane comes to a stop, its final speed is 0 m/s.
[tex]KE_{\text{final}} = \frac{1}{2} m (0)^2 = 0 \, \text{J}[/tex]
3. Calculate the change in kinetic energy (ΔKE):
[tex]\Delta KE = KE_{\text{final}} - KE_{\text{initial}} \\\\\Delta KE = 0 \, \text{J} - 57,154,000 \, \text{J} \\\\\Delta KE = -57,154,000 \, \text{J}[/tex]
4. The work done by nonconservative forces (W):
The work done by nonconservative forces is equal to the negative of the change in kinetic energy (since they are doing work to stop the airplane).
[tex]W = -\Delta KE \\\\W = -(-57,154,000 \, \text{J}) \\\\W = 57,154,000 \, \text{J}[/tex]
Therefore, the work done by nonconservative forces in stopping the airplane is [tex]{57,154,000 \, \text{J}}[/tex] .
Which of the following materials is likely to be the best conductor?
iron
sulfur
carbon
tin
Answers
Answer: Option (a) is the correct answer.
Explanation:
Metals are the substance which have excess of electrons. Therefore, they are good conductors of heat and electricity as they have mobile electrons.
Out of the given options, iron is a transition metal which are good conductors of heat and electricity.
Sulfur and carbon are non-metals, therefore, they are bad conductors of heat and electricity.
Tin is a poor metal so it will not conduct electricity effectively as compared to iron.
Thus, we can conclude that out of the given options, iron is likely to be the best conductor.
Two charged objects of +2Q and +1Q are placed a distance d from one another. The force between the objects in measured as 2F. If the charge on BOTH objects id doubled, what will the force between them be?
Answers
When the charge on both the given objects is doubled, Coulomb's Law indicates that the electrostatic force will become four times greater, resulting in a new force of 8F.
The original question asks about the effect on electrostatic force between two charged objects if both of their charges are doubled.
In the given situation, if we double the charge on both objects (from +2Q to +4Q and from +1Q to +2Q), then the product of the charges becomes 4 times greater because (4Q * 2Q) is 4 times (2Q * 1Q).
Therefore, if the force was initially measured as 2F, after doubling both charges, the force will become 4 times bigger, which is 8F.
This is represented by the option: c.
A soccer player kicks a soccer ball at +10.0 m/s at an angle of 60°. What are the horizontal and vertical components of velocity of the kick?
Answers
Answer:
Horizontal component: [tex]V_{x}=+5m/s[/tex]
Vertical component: [tex]V_{y}=+8.66m/s[/tex]
Explanation:
We have the launch speed [tex]V =+ 10m/s[/tex] and the angle of 60°, so the components of the speed [tex]V_{x}[/tex] and [tex]V_{y}[/tex] are those shown in the attached image.
[tex]V_{x}[/tex] which is the horizontal component of the velocity can be found by multiplying the cosine of the angle by the initial velocity:
[tex]V_{x}=+10m/s(cos60)\\V_{x}=+10m/s(0.5)\\V_{x}=+5m/s[/tex]
[tex]V_{y}[/tex] which is the verticalcomponent of the velocity is found by multiplying the sine of angle by the initial velocity
[tex]V_{y}=+10m/s(sin60)\\V_{y}=+10m/s(0.866)\\V_{y}=+8.66m/s[/tex]
In summary:
Horizontal component: [tex]V_{x}=+5m/s[/tex]
Vertical component: [tex]V_{y}=+8.66m/s[/tex]
Which example provides the most complete description of an object's motion?
1. The ballerina rotated 10 times in 2 minutes.
2. Bobby threw a Frisbee 10 m through the hoop.
3. The turtle took 20 minutes to make it to the other side of the road.
4. The hiker followed a road heading north for 2 miles in 30 minutes.
Answers
Answer:
The hiker followed a road heading north for 2 miles in 30 minutes.
Explanation:
In order to describe the motion of an object, distance covered and time taken must be required. The total path covered by an object is called the distance travelled.
The hiker followed a road heading north for 2 miles in 30 minutes. This describes the motion of hiker. The motion shows how fast the hiker is moving.
Distance, d = 2 miles = 3218.6 m
times, t = 30 minutes = 1800 seconds
So, we can say that the hiker is moving with a speed of 1.78 m/s in north direction.
Hence, this is the required solution.
Answer:
In this case in option 4:
The hiker followed a northbound road for 2 miles in 30 minutes.
Explanation:
Hello ! Let's solve this!
To know the description of a movement we have to know the distance it travels and the time it takes to travel it.
In this case in option 4:
The hiker followed a northbound road for 2 miles in 30 minutes.
Distance: 2 miles
time: 30min
Then we can calculate the speed of the hiker
a baseball pitcher throws a fastball at 42 meters per second. if the batter is 18 meters from the pitcher, approximately how much time does it take for the ball to reach the batter?
Answers
less than half of a second
The time taken by the ball to reach the batter is 0.42 seconds
The baseball pitcher throws a fastball at 42 m/s
The batter is about 18 meters from the pitcher
Therefore the time for the ball to reach the batter can be calculated as follows;
= 18/42
= 0.42 secs
Hence the time taken by the ball to reach the batter is 0.42 seconds
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What process occurs when all of the energy from light waves is transferred to a medium?
Answers
Answer:
absorption
Explanation:
How does the strength of an electromagnet depend on the current and the number of turns in the coil?
Answers
They are directly proportional to strength of Electromagnet.
Hope this helps!
Strength of Electromagnet increases when either the "Current" or "Number of turns in a coil" increases.
They are directly proportional to strength of Electromagnet.
Explanation:
To compile, the power or intensity of a coils magnetic field depends on the following circumstances. The number of turns of wire within the coil. The amount of current running in the coil. An electromagnet is a temporary magnet; the magnetic field only survives when an electric current is running through it. The power of the electromagnet depends on how many coils you wind around and how great the voltage is.
A roller coaster car is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the value of its centripetal acceleration at that point?
Answers
a. The value for the centripetal acceleration is g downward.
(correct answer on plato just did the mastery for this one)
At the top of the loop, where a roller coaster car is just maintaining contact with the track, its centripetal acceleration equals the acceleration due to gravity, which is 9.8 m/s².
Explanation:The value of the centripetal acceleration at the top of the loop, where a roller coaster car just maintains contact with the track, is equal to the acceleration due to gravity, which is 9.8 m/s². This can be deduced from the balancing forces at the top of the loop. In this situation, the force due to gravity is acting downwards while the centripetal force is also acting downwards - directed towards the center of the circular path. Therefore, these forces must match at the top of the loop for the car to just maintain contact with the track. This gives us the equation for centripetal acceleration, ac = g , where ac is the centripetal acceleration and g is the acceleration due to gravity.
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two vectors A and B have components (0,1) and (-1,3), respectively. What is magnitude of the sum of these two vectors?
a) 3.2
b) 4.1
c) 3.9
d) 2.8
Answers
(0 - 1, 1 + 3)
-1 , 4
magnitude = √(1² + 4²)
magnitude = 4.12
The answer is B
Most of the Earth's volcanoes occuWhen fossils or minerals form, certain unstable elements are sometimes locked into them. The proportion of these unstable elements gradually decreases over time as they decay into other materials in a predictable way. Scientists use the rate at which such unstable elements decay to determine when the fossils or minerals formed. The technique described above is known as as
Answers
Radioactive dating, is your answer.
Which best supports the idea that the surface of the moon has changed very little?
a) If photographs of the moon were taken millions of years ago, the surface would look the same.
b) Because the moon does not have a large iron core, it is not possible for geologic events to occur on the moon.
c) Because the moon has no atmosphere, it is not possible for geologic events to occur on the moon.
d) If one considers the history of the moon, there is only one distinct phase of its development.
Answers
Atmosphere is related to geological change because of things such as wind and water erosion that over time change the landscape, and there's neither on the moon. It's just a floating rock.
Which of Newton's Three Laws does the following statement satisfy?
For every action there is an equal and opposite reaction.
A
Newton’s First Law
B
Newton’s Second Law
C
Newton’s Third Law
Answers
What would a drummer do to make the sound of a drum give a note of lower pitch?
a. hit the drum skin with a larger force b. hit the drum skin with a smaller force
c. hit the drum skin nearer the edge d. loosen the drum skin ...?
Answers
Hitting the drum skin nearer the edge is what would a drummer do to make the sound of a drum give a note of lower pitch.
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In 1831, Michael Faraday was the first to realize that an electric current could be induced by passing a magnet through a coil of copper wire. Which factor is MOST essential for the induction of the electric current?
Answers
Answer:
D
Explanation:
it is the correct answer on usa test prep
How is light used to study space? IN YOUR OWN WORDS
Answers
Hope you will find it helpful!
Which type of radiation is used to make images of bones inside the body?
Answers
A rectangular pool has a volume of 375 m3. the pool is 10 m long and 5 m wide. how deep is the pool? 7.5 m 3,750 m 75 m
Answers
A bullet is fired horizontally from the top of a building with a muzzle velocity of 150 m/s.A similar bullet dropped from the top of the same building, takes 4 sec to reach the ground. How far forward does the first bullet go before it hits the ground?
Answers
Final answer:
The horizontal distance traveled by the bullet before hitting the ground is 600 meters.
Explanation:
To determine how far forward the bullet goes before it hits the ground, we can use the fact that both the horizontally fired bullet and the dropped bullet hit the ground after a certain time. The dropped bullet takes 4 seconds to reach the ground, so we can consider its vertical motion using the equation h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time. Plugging in the values, we get 0 = 0.5 * 9.8 * 4^2, which gives us h = 78.4 meters.
Since the horizontally fired bullet has the same horizontal velocity as the dropped bullet, it would take the same time to reach the ground. This means that the horizontally fired bullet travels a horizontal distance equal to its horizontal velocity multiplied by the time it takes to reach the ground. Plugging in the values, we get d = 150 * 4 = 600 meters.
Therefore, the first bullet travels 600 meters forward before hitting the ground.
The bullet fired horizontally travels 600 meters before hitting the ground because it takes the same 4 seconds as the dropped bullet to reach the ground, and it travels at a horizontal velocity of 150 m/s.
Step-by-Step Explanation:
Calculate the horizontal distance using the formula: distance = velocity x time.Here, the muzzle velocity of the bullet is 150 m/s and the time is 4 seconds.Distance = 150 m/s * 4 s = 600 meters.Conclusion:
The bullet fired horizontally travels 600 meters before it hits the ground.
Which voice can produce a pitch that has a speed of 343 m/s and a wavelength of 0.68m?
Answers
A cold beer initially at 35ºF warms up to 40ºF in 3 min while sitting in a room of temperature 70ºF. How warm will the beer be if left out for 20 min
Answers
Final answer:
Using Newton's law of cooling, we can calculate that the beer will be approximately 60.4ºF if left out for 20 minutes.
Explanation:
To calculate the final temperature of the beer after being left out for 20 minutes, we can use Newton's law of cooling. This law states that the rate of heat loss of an object is proportional to the temperature difference between the object and its surroundings. In this case, the initial temperature of the beer is 40ºF and the room temperature is 70ºF. Let's determine the constant of proportionality, k, first:
k = (T2 - T1) / t = (70 - 40) / 3 = 10
Now we can use the formula to find the final temperature, T3, after 20 minutes:
[tex]T3 - 70 = (40 - 70)e^(-10(20/3))[/tex]
[tex]T3 - 70 = -30e^(-20/3)[/tex]
[tex]T3 = 70 - 30e^(-20/3)[/tex]
Using a calculator, we can find that T3 is approximately 60.4ºF.
A large region of gas and dust that may contain as many as one million solar masses is called a _____.
a. galaxy
b. protostar
c. supernova remnant
d. giant molecular cloud
Answers
Answer:
a giant molecular cloud.
Explanation:
The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?
Answers
The inequality x² + 2x - 168 ≤ 0 can be used to determine the possible lengths of the base of a triangle when the height is 4 inches greater than twice the base and the area is no more than 168 square inches.
To find the possible lengths of the base of a triangle where the height is 4 inches greater than twice the base and the area is no more than 168 square inches, we start with the formula for the area of a triangle:
Area = (1/2) × base × height.
Let the base be x. Thus, the height can be expressed as 2x + 4. Therefore, the area equation becomes:
(1/2) × x × (2x + 4) ≤ 168
To simplify this, multiply both sides by 2:
x(2x + 4) ≤ 336
Expanding and rearranging the terms gives:
x² + 4x ≤ 336
Subtract 336 from both sides to form a quadratic inequality:
x² + 4x - 336 ≤ 0
Divide the entire inequality by 2 to simplify:
x² + 2x - 168 ≤ 0
This is the inequality that can be used to find the possible lengths of the base of the triangle.
Conceptual Question 8.09osama wadi
Part A
In a perfectly ELASTIC collision between two perfectly rigid objects
the momentum of each object is conserved.
both the momentum and the kinetic energy of the system are conserved.
the kinetic energy of the system is conserved, but the momentum of the system is not conserved.
the kinetic energy of each object is conserved.
the momentum of the system is conserved but the kinetic energy of the system is not conserved.
...?
Answers
In a perfectly ELASTIC collision between two perfectly rigid objects,
the momentum of each object is conserved.
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Will a solid metal sphere hold a larger elaectric charge than a hollow sphere of the same diameter?Where does the charge reside in each case? ...?