College Physics

Question

A ball is thrown horizontally from the top of
a building 100 m high. The ball strikes the
ground 54 m horizontally from the point of
release.
What is the speed of the ball just before it
strikes the ground?
Answer in units of m/s

Answer 1

The key point here is that velocity is a vector.  Hence it has a horizontal speed (v) and a vertical speed (u) that are independent.  So how long will it take the ball to fall 100 m?

 

d = (1/2)gt²

100 = (1/2)(9.8)t²

20.41 = t²

4.52 = t

 

So horizontally, the ball moves at a constant velocity, v, for t = 4.52 sec:

 

d = vt

54 = v(4.52)

11.95 m/s = v  -->  This is the speed at which the ball was thrown

 

The vertical speed of the ball is:

 

u = gt

u = (9.8)(4.52)

u = 44.3 m/s

 

The ball's total speed is:

 

V = √(v²+u²)

V = √(11.95²+44.3²)

 

Use your calculator to get the answer (in m/s).