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## 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 v

_{0}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) = v

_{0}cosΘ t

y(t) = v

_{0}sin Θ t - 1/2 g t

^{2}

## The Attempt at a Solution

0 = v

_{0}sinΘ t -1/2 g t

^{2}

1/2 g t

^{2}= v

_{0}sinΘ t

1/2 gt = v

_{0}sinΘ

t = 2 v

_{0}sin Θ/ g

x = 2 v

_{0}

^{2}cosΘ sinΘ / g

x = 2 v

_{0}

^{2}cos45 sin45 / g

x= 2 v

_{0}

^{2}* .5 / g

Second ball( the one that bounces with two parabolas)

x/2 = 2v

_{0}cosΘsinΘ / g

v

_{0}

^{2}cosΘ sinΘ/g = 2 v

_{0}

^{2}*.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