Here's the problem:

"Every once in a while a bird will get hit by a baseball during a baseball game. The longest home runs in baseball land about 500 feet (which is 152.4 meters) from home plate. If these balls leave the bat at a 45 degree angle to maximize their distance, what is the minimum safe height in meters for birds around baseball stadiums?"

Then follows a picture of a parabola with the height of the apex labeled H.

This question seems confusing to me since the answer that successfully answers the question is the value of H. This can be done w/ simple calculus, no physics whatsoever.

I think a more appropriate answer would be to solve for the speed of the ball at launch, recognizing that that energy could be applied in the vertical direction, utilize that to determine a maximum height of the ball if hit straight up. Note this solution actually uses some physics.

Alternatively, the problem could be restated to "what is the minimum safe height in meters for birds to avoid these home runs?" (or of course get rid of the 'bird' part completely)

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TopNewestJeff,

It certainly can be done with calculus, once you realize that the trajectory of the ball is actually a parabola. The physics comes in only in determining the shape of the trajectory. From your text above, and correct me if I'm wrong, it appears that you looked at the picture and assumed that it was a parabola, which isn't quite justified - looking at a picture and assuming a particular mathematical form can be a little dangerous.

As an aside, you are absolutely correct that in general once you have the equation of motion for a particle, the physics part is over. Everything else is just math (usually solving a differential equation). But the physics to determine accurately what the equation of motion is can be complicated!

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