Projectile Motion: Determine v_0 to go over a fence

[CapnKrump]

Homework Statement

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.

Homework Equations

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

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?

 

[Dr. Courtney]

Yep, it's complicated.

 

[CapnKrump]

it's complicated.

The problem, the answer, or both?

 

[Dr. Courtney]

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

 

[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).
Please post your working.