# Homework Help: Projectile motion and initial speed

1. Oct 17, 2009

### juliorevka

1. The problem statement, all variables and given/known data

From a height of 23 m, a ball is thrown horizontally. If it hits the ground with a speed that is three times its initial speed, what is the initial speed?

vertical: a = -9.8, x = -23, t = ?, V0=?, V = 3V0
horizontal: ?
x is displacement

2. Relevant equations
Possibly relevant:
V = Vo + at
x-x0 = Vot + .5at2
x-x0 = Vt - .5at2
x-x0 = .5(V0+ v)t
V2 = V02 + 2a(x-x0)

3. The attempt at a solution
Seems simple, but I have tried and cannot do this problem. Seems like there is not enough info.

Solving the system of the following equations for vertical motion
x-x0 = Vot + .5at2
x-x0 = Vt - .5at2
found that t = 2.1447, but I am not sure if this is correct. After that I just didn't know what to do. For horizontal movement, it seems like there is only time and the fact that the final velocity is 3 times the initial velocity.

2. Oct 17, 2009

### Jack21222

Your time for t is basically correct, though the number I got is slightly off. I get 2.17 for some reason.

Using t, you can also find the final velocity in the y direction.

After that, it's simple vector algebra. You know the Vfx vector and the Vfy vector. You know that the Vf vector is 3 times the Vox vector.

So, you have enough information. Just set up the vectors.