Download 1. A skydiver jumps out of an aircraft. His initial vertical velocity is

1.
A skydiver jumps out of an aircraft. His initial vertical velocity is zero and his initial acceleration of 9.8 ms-2.
i) What does the minus sign on the acceleration indicate?
ii) What is meant by an acceleration of 9.8 ms-2?
iii) Assuming the acceleration of the skydiver stays constant calculate the vertical velocity of the
skydiver after 2.0 s. Ans: -19.6 ms-1.
iv) Assuming the acceleration of the skydiver stays constant calculate the displacement of the
skydiver after 2.0 s. Ans: -19.6 m.
v) In reality the acceleration of the skydiver decreases. Explain why. Your answer must include the
words weight and air resistance.
vi) Eventually the skydiver falls with a constant velocity. Explain why. Your answer must include the
word ‘balanced’.
2.
(A) The F-t graph below shows the force on a football due to a footballer’s foot.
Explain why the force on the ball rises and falls. (this can be explained by considering the
deformation of the ball as the foot sinks into it).
Force on football
Time force acted on football
(B) Suppose the maximum force on a stationary 450.0 g ball is 100.0 N and the duration of the force
acting on the ball is 0.4 s.
i) Draw the idealised F-t graph for this ball. Ans: Same shape as above with maximum force equal
to 100N and time equal to 0.4 s.
i) Calculate the magnitude of the impulse on the ball. Ans: 20 Ns
ii) Write down the change of momentum of the ball. Ans: 20 kgms-1.
iii) Write down the magnitude final momentum of the ball. Ans: 20 kgms-1.
iv) Calculate the speed of the ball at the instant it leaves the club. Ans: 44.4 ms-1.
v) Suppose the footballer kicked a stationary softer ball with the same mass. If this ball left the foot
with the same speed, draw its force-time graph. Ans: Same shape as above with maximum force
less than 100N and time greater than 0.4 s. Same impulse and change in momentum (area) in each
case.
3. For this problem use only vertical quantities when calculating values relevant to the vertical
nature of the motion. For example, for height risen or time to rise to that height the only relevant
quantities are the vertical acceleration (always -9.8 ms-2) and the initial vertical velocity. Similarly for
questions relevant to the horizontal nature of the motion only use horizontal quantities. So, for
horizontal distance travelled the only relevant quantities are the horizontal velocity and the time
which is usually worked out worked out using vertical information.
40.0 ms-1
(A)
A ball is launched as shown. The only information you are given is the initial velocity of the ball.
i) Calculate the initial vertical velocity of the ball. Ans: 34.6 ms-1
ii) Calculate the time taken to reach its highest point. Ans: 3.5 s
iii) Calculate the maximum height the ball rises to. Ans: 60.5 m
iv) Calculate the total time for the flight. Ans: 7.0 s
v) Calculate the horizontal velocity of the ball. Ans: 20.0 ms-1
vi) Calculate the horizontal distance travelled by the ball. Ans: 140.0 m
vii) Only one of the above vector quantities will change during the flight which is it? Ans:
The ball’s vertical velocity
vi) What will the ball’s minimum velocity be and where will it occur. Ans: 20 ms-1 to the
Right at the top of its flight.
(B)
Suppose the ball was projected with a smaller angle but with the same initial speed. What effect, if
any, will this affect…
i)
ii)
iii)
iv)
v)
The initial vertical velocity of the ball. Ans: Less
The maximum height the ball rises to. Ans: Less
The total time for the flight. Ans: Less
The horizontal velocity of the ball. Ans: Greater
Why is in not possible to predict the change will have on the horizontal distance?
4. A fast moving subatomic particle has an average lifetime of 2.0s. However Benny, viewing the
particle from a stationary position on Earth, finds that its lifetime is a bit longer. Nestor explains to
him that this is due to time dilation.
i) What is meant by time dilation?
ii) If the particle is travelling at 0.75 c, then calculate its lifetime according to Benny. Ans 3.0 s
5. A police car travelling at 22 ms-1 is about to pass a pedestrian. If the car’s siren produces a 600
Hz sound and the speed of sound in air is 330 ms-1 then calculate the frequency heard by the
pedestrian as the ambulance i) approaches and ii) retreats from him. Ans: i) 642.8 Hz, ii) 562.5 Hz.
6. A distant star with a Hydrogen atmosphere is observed by astronomers. The blue light in the
Hydrogen spectrum is 434 nm as measured on Earth but is measured as 454 nm from the star.
i) Calculate the redshift for this wavelength. Ans 0.05.
ii) Calculate the speed at which the star is receding from Earth Ans: 1.5 x 107 ms-1