Question

A plane drops a rubber raft to the survivors of a shipwreck. The plane is flying at a height of 1960 m and with a speed of 109 m/s. The raft lands next to the survivors. Ignoring air resistance, how far away from the shipwreck was the plane when the raft was dropped? (g = 9.8 m/s2) (Round your answer to a whole number).

Answer 1

In this case the rubber raft has horizontal and vertical motion.

Considering vertical motion first.

We have displacement
`s = ut +(1)/(2)at^2`, u = Initial velocity, t = time taken, a = acceleration.

In vertical motion

s = 1960 m, u = 0 m/s, a = 9.81
`m/s^2`

`1960 = 0*t+(1)/(2) *9.81*t^2\\ \\ t = 20 seconds`

So raft will take 20 seconds to reach ground.

Now considering horizontal motion of raft

u = 109 m/s, t = 20 s, a = 0
`m/s^2`

So
`s = 109*20+(1)/(2) *0*20^2 = 2180 m`

So shipwreck was 2180 meter far away from the plane when the raft was dropped.