Questions

Q1. 

A student uses a lamp and a light sensor as a light gate connected to a data logger and computer to determine the speed of a falling object. He drops a small cylinder through a clear plastic tube. The light gate and data logger measure the time of fall of the cylinder and the speed is calculated.

The student repeats the experiment five times and records the results in a table.

The student incorrectly includes all the values when calculating the mean speed. A second student thinks that the true value of the mean speed is different.

Explain whether the second student is correct.

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(Total for question = 2 marks)

Q2. 

The diagram shows a diver of weight 680 N on a diving board.

The diving board has a length L of 3.6 m and is fixed at the end labelled X. It is supported at position Y which is 0.9 m from X. The diving board is uniform and has a weight of 390 N.

By taking moments about X, determine the upward force exerted by the support at Y on the diving board.

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Force = ...........................................................

 

(Total for question = 5 marks)

Q3. 

A student rows across a river heading from point A. Her boat is headed in a direction at right angles to the bank and she rows through the water at a constant speed of 1.5 s−1

The river flows with a current of 1.1 m s−1

(a)  Calculate the velocity of her boat relative to the riverbank.

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Magnitude of velocity = ...........................................................

Angle of velocity to the riverbank = ...........................................................

(b)  Another student also rows through the water at a constant speed of 1.5 m s−1 and heads their boat in a direction at 65° to the riverbank.

On the grid below draw a scaled vector diagram to determine the velocity of the boat.(3)

Magnitude of velocity = ...........................................................

Angle of velocity to the riverbank = ...........................................................

 

(Total for question = 7 marks)

Q4.*  In 2012 Neil Armstrong, the first man to step on the moon during the Apollo 11 lunar mission, died at the age of 82.

During this mission, a planned explosion caused the separation of the module in which Armstrong was travelling and the final-stage rocket. This explosion resulted in an increase in the speed of the module.

Discuss how the conservation of momentum and the conservation of energy apply to this situation.

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(Total for Question = 5 marks)

Q5. 

The photograph shows cars travelling on a straight section of a motorway.

The maximum speed limit on a motorway in the U.K. is 31ms−1.

A car is travelling along the motorway at 31ms−1. The driver sees stationary traffic 180 m ahead. After 0.6 s the driver reacts by applying a constant braking force that stops the car in 10 s.

(i)  Draw a velocity-time graph of the car's motion, from the instant the driver sees the stationary traffic until the car stops.

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(ii)  Analyse the data to determine whether the car stops without colliding with the stationary traffic.(2)

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(Total for question = 3 marks)

Q6.The photograph shows an athlete performing a long jump.

At take-off his horizontal speed is 8.0 m s−1 and his vertical speed is 2.8 m s−1.

(a)  Show that the total time the athlete spends in the air is about 0.6 s.

Assume that his centre of gravity is at the same height at take-off and landing.

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(b)  Calculate the horizontal distance jumped by the athlete.

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Horizontal distance = ...........................................................

(c)  In reality, when the athlete lands his centre of gravity is 50 cm lower than its position at take-off.

Calculate the extra horizontal distance this enables the athlete to jump.

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Extra horizontal distance = ...........................................................

(Total for Question = 9 marks)

Q7. 

The monkey and hunter is a thought experiment to illustrate the independence of the horizontal and vertical motion of a projectile.

A student models the experiment by projecting a table tennis ball horizontally at a toy monkey. The ball and monkey are initially at the same height, 0.25 m, above the bench.

The monkey drops at the instant the ball is projected. The monkey and the ball will always meet irrespective of their horizontal separation.

(a)  (i)  Show that the time taken for the ball to fall to the bench is about 0.2 s.

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(ii)  The ball is projected with a horizontal velocity of 2.6 m s−1

Calculate the horizontal distance that the ball should travel if the ball is to hit the monkey as it reaches the bench.

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Horizontal distance = ...........................................................

(b)  A variation of this experiment is where the monkey is initially higher so that the ball has to be projected upwards towards the monkey. The two objects will still always meet.

(i)  Complete the diagram above to show the paths of the ball and the monkey.(2)

(ii)  The ball is projected with a velocity of 3.0 m s−1 at an angle of 20° to the horizontal. If the monkey is at a horizontal distance of 0.50 m, how far will it have fallen when it meets the ball?

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Distance fallen = ...........................................................

 

(Total for question = 9 marks)