Projectile Motion: Determine v_0 to go over a fence

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
Gold Member
2020 Award
Yep, it's complicated.

it's complicated.

The problem, the answer, or both?

Dr. Courtney
Gold Member
2020 Award
The best double check is to plot the resulting parametric equations with real numbers and see if it clears the fence.

haruspex