Projectile Motion: Determine v_0 to go over a fence

  • #1
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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?
 

Answers and Replies

  • #3
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it's complicated.

The problem, the answer, or both?
 
  • #4
Dr. Courtney
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The best double check is to plot the resulting parametric equations with real numbers and see if it clears the fence.
 
  • #5
haruspex
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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.
 

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