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Physics problems: kinematics

Free fall motion

 

Problem 2.

A child throws a ball downward from a tall building. Note that the ball is thrown, not dropped and disregard air resistance. What is the acceleration of the ball immediately after it leaves the child's hand?

Solution

 

Problem 4.

An archer shoots an arrow with a velocity of 30 m/s at an angle of 20 degrees with respect to the horizontal. An assistant standing on the level ground 30 m downrange from the launch point throws an apple straight up with the minimum initial speed necessary to meet the path of the arrow. What is the initial speed of the apple and at what time after the arrow is launched should the apple be thrown so that the arrow hits the apple?

Solution

 

Problem 11.

From the dimensional analysis find the time t it takes for a ball to fall from a height h.

Solution

 

Problem 13.

How high can a human throw a ball if he can throw it with initial velocity 90 mph.

Solution

 

Problem 22.

A ball is thrown vertically upward with a speed of 25.0m/s.

(a) How high does it rise?

(b) How long does it take to reach its highest point?

(c) How long does the ball take to hit the ground after it reaches its highest point?

(d) What is its velocity when it returns to the level from which it started?

Solution

 

Problem 31.

A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails. 

(a) How long does it take it to reach 1000m?

(b) How high does the missile go?

(c) How long does it take for it to fall back to the earth? 

(d) How long does it stay in the air?

(e) How fast is it going when it hits the ground?

Solution

 

Problem 33.

A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at until it reaches an altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.

(a)  How long was the rocket above the ground?

(b)  What is the maximum altitude?

(c) What is the velocity just before it collides with the ground?

Solution

 

 

 

 

 

Problem 34.

An object is fired straight up at a speed of 9.8m/s. Compute its maximum altitude and the time it takes to reach that height. Ignore air resistance.

Solution

 

Problem 35.

A rock is dropped from rest into a well.

(a) The sound of the splash is heard 4 s after the rock is released from rest.

How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s).

(b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?

Solution

 

Problem 36.

A ball is thrown upward with initial velocity v.  What is the change in speed on the way up? What is the change in speed on the way down? Disregard air resistance.

Solution

 

Problem 46.

A flowerpot falls from a windowsill 25.0 m above the sidewalk.      

(a) how fast is the flowerpot moving when it strikes the ground?

(b) how much time does a passerby on the sidewalk below have to move out of the
        way before the flowerpot hits the ground?

Solution

 

Problem 47.

A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s.

(a) what will the ball\'s speed be when it returns to its starting point?

(b) how long will the ball take to reach its starting point?

Solution

 

Problem 54.

On the moon, an object is dropped from a height of 2 m. The acceleration of gravity on the moon is . Determine the time it takes for the object to fall to the surface of the moon.

Solution

 

 

 

 

 

Problem 55.

A coin is dropped from a 400 m high tower. What is the coin's velocity when it hits the ground? How long does it take to get there?

Solution

 

Problem 71.

A stone falls freely from rest for 10 s. What is the stones displacement during this time.

Solution

 

Problem 73.

A rock is shot up vertically upward from the edge of the top of the building. The rock reaches its maximum height 2 s after being shot. Them, after barely missing the edge of the building as it falls downward, the rock strikes the ground 8 s after it was launched. Find

(a) upward velocity the rock was shot at;

(b) the maximum height above the building the rock reaches; and

(c) how tall is the building?

Disregard air resistance.

Solution

 

Problem 77.

Calculate the hang time of an athlete who jumps a vertical distance of .9 meters considering the acceleration of gravity is

Solution

 

Problem 88.

A stone is thrown vertically upward was noted having a velocity of 15 m/s after covering 2/3 its maximum height.
(1) What is the total height reached by the stone?
(2) With what velocity was it thrown?

Solution

 

Problem 89.

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 37.0 m -tall building. The rocket's engine produces a horizontal acceleration of , in the same direction as the initial velocity, but in the vertical direction the acceleration is , downward.  Air resistance can be neglected. How long is the rocket in the air before it hits the ground?

Solution

 

 

 

 

 

Problem 90.

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 37.0 m -tall building. The rocket's engine produces a horizontal acceleration of , in the same direction as the initial velocity, but in the vertical direction the acceleration is , downward.  Air resistance can be neglected. How far does the rocket travel in horizontal direction before it hits the ground?

Solution

 

Problem 91.

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 37.0 m -tall building. The rocket's engine produces a horizontal acceleration of  (time dependent acceleration), in the same direction as the initial velocity, but in the vertical direction the acceleration is , downward.  Air resistance can be neglected. How long is the rocket in the air before it hits the ground?

Solution

 

Problem 94.

An object thrown upwards with a velocity u from the top of a tower of height H reaches the ground in  seconds. When thrown downwards with the same speed it reaches the ground in  seconds. When dropped from the top of tower it reaches in  seconds. Show that .

Solution

 

Problem 97.

An astronaut jumps from an airplane. After he had fallen 40 m, then his parachute opens. Now he falls with a retardation of  and reaches the earth with a velocity of 3.0 m/s. What was the height of the aeroplane?

Solution

 

Problem 98.

A ball is thrown vertically upward at 20 m/s ignoring air resistance and taking . Calculate:
(1) maximum height.
(2) time taken to reach the maximum height.
(3) time taken to return to starting point.

Solution

 

Problem 105.

A student throws his test paper up in the air (neglecting air resistance) with an initial speed of 8.10 m/s. How long does it take until the paper is headed downward at a speed of 3.23 m/s?

Solution

 

Problem 106.

A ball is thrown upward from the top of a 31.0 m tower on an unknown planet (gravitational acceleration is unknown) with an initial speed of 12.0 m/s and hits the ground with a speed of 52.0 m/s. How long was the ball in flight?

Solution

 

Problem 107.

A skier leaves the end of a horizontal ski jump at 22.0 m/s and falls 3.20 m before landing. Neglecting friction, how far horizontally does the skier travel in the air before landing?

Solution

 

Problem 112.

A body is thrown vertically up from the ground with a speed time and it reaches maximum height h at time initial. What is the height to which it would have risen at time

Solution

 

 

 

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