8 A tennis ball machine fires a ball vertically upwards at time
t=0 at 19.6 m/s. Assume that air resistance is negligible and
take g =9.8 m/s
a) Calculate the displacement and velocity of the ball at
t=1.0 s, 2.0 s, 3.0 s and 4.0 s.
b) Use your answers to part a) to draw
i) a graph of displacement against time for the ball
ii) a graph of velocity against time for the ball.

  table and graph are attached

Explanation:

a) The velocity of the ball will be ...

  v(t) = v0 -at

  v(t) = 19.6 -9.8t

The position of the ball will be the integral of this:

  h(t) = ∫v(t)·dt = 19.6t -(1/2)(9.8t^2)

The attached table calculates the vertical position in meters for the required times.

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b) Graphs of displacement (h(t)) and velocity (h'(t)) are shown in the attachment.

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