Question

An airplane is flying horizontally with a constant velocity of 245 m/s. While in flight, the airplane drops a package when it is 1.5 km above the ground. What is the Horizontal velocity and the initial vertical velocity? How fast will the package be falling down when it hits the ground? How long will it take the package to hit the ground? What is the horizontal displacement the package over this time?

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.

   Initial vertical velocity = 0 m/s

   Initial horizontal velocity = 245 m/s

In vertical motion

    s = 1.5 km = 1500 m, u = 0 m/s, a = 9.81 $m/s^2$

    $1500 = 0*t+\frac{1}{2} *9.81*t^2\\ \\ t = 17.49 seconds$

So package will take 17.49 seconds to reach ground.

Now we have v = u+at, where v is the final velocity

Here u = 0 m/s, a= 9.81 $m/s^2$ and t = 17.49 seconds

Substituting

     v = 0+9.8*17.49 = 171.402 m/s

The speed with which the package strikes the ground = 171.402 m/s.

Now considering horizontal motion of package

u = 245 m/s, t = 17.49 s, a = 0$m/s^2$

So $s = 109*17.49+\frac{1}{2} *0*17.49^2 = 1906.41 m$

So package falls 1906.41 meter far away from the position of plane when the package was dropped.