Question

Motion along a curve, projectiles.

The wall in Fenway Park is 37 feet high and 315 feet away from home plate. A baseball hit 3 feet above the ground at an angle 22.5 will just go over is V_o = ______. The time to reach the wall is t = _____ .

Check my solution please?

Answer 1

\[\large x(t) = (v_o cos \alpha)t\]
\[\large y(t) = (v_o sin \alpha)t - \frac{1}{2}gt^2\]

We want x(t) to be 315 so

\[\large 315 = (v_o cos(22.5))t\]
solve that for v_o
\[\large v_o = \frac{315}{tcos(22.5)}\]

sub that in for \(\large v_o\) in y(t) knowing we want y(t) to be ????37??? or ???34??? I did 37 for this
\[\large 37 = ((\frac{315}{tcos(22.5)}) sin (22.5))t - \frac{1}{2}(9.8)t^2\]
Simplify a bit
\[\large 37 = 315tan(22.5) - \frac{1}{2}(9.8)t^2\]
\[\large 37 - 315tan(22.5) = - \frac{1}{2}(9.8)t^2\]
\[\large 2(37 - 315tan(22.5)) = -9.8t^2\]
\[\large t = \sqrt{\frac{2(37 - 315tan(22.5))}{-9.8}}\]
\[\large t = 4.37\]

And I solve that for velocity etc and I get an answer that checks out for the height being 37

HOWEVER, am I supposed to use the fact that the height started out at 3 feet off the ground and only had to travel 34 feet?

Answer 2

You can use \(x(t)\) to find how long it will take ball to reach the wall, which is 315 feet away from home plate.