Projectile Motion of thrown ball

[Austin Chang]

Homework Statement

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)

Homework Equations

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

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 don't know what went wrong in problem

 

[haruspex]

x/2 = 2v0cosΘsinΘ / g
v0² cosΘ sinΘ/g = 2 v0²*.5/g

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.)

 

[Austin Chang]

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.)

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?

 

[haruspex]

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?

Yes.