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  $s = ut +\frac{1}{2}at^2$, u = Initial velocity, t = time taken, a = acceleration.

In vertical motion

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

    $1960 = 0*t+\frac{1}{2} *9.81*t^2\\ \\ t = 20 seconds$

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 $s = 109*20+\frac{1}{2} *0*20^2 = 2180 m$

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