Projectile Motion: Determine v_0 to go over a fence

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1. Feb 4, 2016

CapnKrump

1. The problem statement, all variables and given/known data
You're the new home run hitter for a baseball team. Your job is to hit the ball over a fence D away and H high. For a given angle θ calculate the speed with which the ball must be hit v0 to go over the top of the fence.

2. Relevant equations
1. y = y0+(v0*sinθ)-½gt2
2. x = v0*t*cosθ

3. The attempt at a solution

I tried using H as my y value from eq. 1 and D as my x value in eq. 2. I solved for v0 in eq. 2 (D/(t*cosθ)), then attempted to eliminate t by solving for it in equation 1 using the quadratic formula. Then I substituted the result into the D/(t*cosθ) equation.

The result is a very bulky equation that I'm unsure is correct. A tutor said my reasoning was sound, and was unable to come up with a more simplified answer himself. What do you guys think? Am I even on the right track here?

2. Feb 4, 2016

Dr. Courtney

Yep, it's complicated.

3. Feb 4, 2016

CapnKrump

The problem, the answer, or both?

4. Feb 4, 2016

Dr. Courtney

The best double check is to plot the resulting parametric equations with real numbers and see if it clears the fence.

5. Feb 4, 2016

haruspex

Your quoted equation for y is missing something. I assume that's just a typo.
I assume H is the height relative to the point of impact, so y0=0.
The only use of t here is to connect the horizontal and vertical motions, so I would start by obtaining a single equation relating x and y, with t absent.
After that it does not look complicated to me. You can get a small simplification by using the formulae for sin(2θ) and cos(2θ).