Question

an airplane is flying horizontally to the right with a speed of 150 kph at an altitude of 503 m when it drops a bomb. at the instant the bomb is dropped, a 3m high truck, traveling to the right with a constant velocity on the ground is 150 m horizontally ahead of the plane. If the bomb is to hit the top of the truck, determine the velocity of the truck.

Answer 1

This is a nice problem. Just give me a couple of minutes to write my answer down.

Answer 2

sure, i will be waiting.

Answer 3

Let's first find the time needed for the bomb to hit the car by considering its vertical motion. By solving the equation \(d=v_it+0.5at^2\) with \(d=503-3\), \(v_i=150 kph=41.67m/s\) and \(a=9.8m/s^2\), we find one positive value of t which is around \(15 sec\).

Answer 4

Now, consider the horizontal motion of the bomb, it should have the same initial velocity as the plane and a zero final velocity. It will hit the car, as I just found, after 15 sec. So, we can find the horizontal distance it will move before hitting the truck. The distance would be, neglecting air resistance, is \(vt=41.67(15)=625 m\)

Answer 5

But the truck was 150 m ahead of the plane, so at this time it should've moved only \(625-150=475 m\). And since its moving in a constant velocity, its velocity would be just the traveled distance over the time, that's \(475/15=31.67 m/s\), or \(114 kph\).

Answer 6

@AnwarA pretty close, but the velocity of the plane is horizontal, and does not affect the time it takes the bomb to fall 500 m.
so d= 0.5 g t^2, where d = (503-3), g apprx 10
t = 10 seconds

Answer 7

Whoops! You're right :D

Answer 8

yes. it's 10.102 sec

Answer 9

anyway, thanks a lot. i got the answer because of the solution you did. :)

Answer 10

Haha! That's good :)