Suppose you are on a platform 27m above the sea and toss a ball directly upwards at

3.5m/s and allow it to fall into the sea.

Some notes

a general equation for rectilinear motion under constant acceleration (for example,

in free fall) is s(t) = s0 +v0t+0:5at2 , where s is displacement or position (use units

of metres here), t is time (in seconds), s0 is initial position (displacement at time

zero), v0 is initial velocity (in m/s), and a is acceleration (in m/s2).

Use one decimal place in calculations and in reporting answers.

Assume air resistance is negligible so that initially only gravity acts on the ball,

imparting an acceleration of -9.8 m/s2.

a) Write down an equation for the ball`s displacement from the platform (in metres)

for time t 0 in

ight

b) What is the instantaneous velocity of the ball 2 seconds into its

ight?

c) Over what time is the ball at least 12m above the sea?

d) A friend in the water throws the ball back to you. If the ball is released 1m above

water level, at what minimum initial velocity must the ball be thrown to reach the

platform?

2018-03-05
Maths