Projectile Motion of thrown ball

  • #1

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 dont know what went wrong in problem
 

Answers and Replies

  • #2
haruspex
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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.)
 
  • #3
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?
 
  • #4
haruspex
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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.
 

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