# Projectile Motion of thrown ball

1. Sep 15, 2016

### Austin Chang

1. The problem statement, all variables and given/known data
A person throws a ball at a 45 degree angle and hits a given target. How much quicker does the ball get to the target if the person instead throws the ball with the same speed v0 but at the angle that makes the trajectory consist of two identical bumps, as shown (Assume unrealistically that there is no loss in speed at the bounce)

2. Relevant equations
x(t) = v0 cosΘ t
y(t) = v0 sin Θ t - 1/2 g t2

3. The attempt at a solution
0 = v0 sinΘ t -1/2 g t2
1/2 g t2 = v0 sinΘ t
1/2 gt = v0 sinΘ
t = 2 v0 sin Θ/ g
x = 2 v02 cosΘ sinΘ / g
x = 2 v02 cos45 sin45 / g
x= 2 v02 * .5 / g
Second ball( the one that bounces with two parabolas)
x/2 = 2v0cosΘsinΘ / g
v02 cosΘ sinΘ/g = 2 v02*.5/g
cosΘsinΘ = 1
2cosΘsinΘ = 2
sin2Θ = 2
sin-1(2) = 2θ
domain error I know why its domain error. Just dont know what went wrong in problem

2. Sep 15, 2016

### haruspex

Check that step. (The first line is missing a power of 2, but that's clearly just a typo, not the error I care about.)

3. Sep 15, 2016

### Austin Chang

Oh lol, that was a silly mistake times 2 instead of divide by 2 Ok I got 15 degrees as an answer. Is that correct?

4. Sep 15, 2016

Yes.