- #1

- 41

- 0

## Homework Statement

In a baseball game, a batter hits the ball at a height of 4.60 ft above the ground so that its angle of projection is 52.0º to the horizontal. The ball lands on the grandstand, 39.0 ft up from the bottom. The grandstand seats slope upward at 28.0º with the bottom seats 358 ft from the home plate. Calculate the speed at which the ball left the bat (ignore air resistance).

## Homework Equations

(1) y - y[itex]_{}0[/itex] = v[itex]_{}0y[/itex]t - 0.5gt^2

(2) x = v[itex]_{}0x[/itex]t

## The Attempt at a Solution

Since x = v[itex]_{}0x[/itex]t, we can rewrite the equation as x = v[itex]_{}0[/itex]cos[itex]\phi[/itex]t

Solve for t, we get t = x / v[itex]_{}0[/itex]cos[itex]\phi[/itex]

v[itex]_{}0y[/itex] = v[itex]_{}0[/itex]sin[itex]\phi[/itex]

Plug these variables to equation 1 and with some algebraic manipulations, you get:

y - y[itex]_{}0[/itex] = (tan [itex]\phi[/itex])x - 0.5 g( x / v[itex]_{}0[/itex]cos[itex]\phi[/itex])^2

Now I have to solve for v[itex]_{}0[/itex].

I derive this equation: v[itex]_{}0[/itex] = x[itex]\sqrt{}g / -2(cos\phi)^2(y - y_{}0 - xtan\phi[/itex])

To save you guys from more work, the given variables are y - y[itex]_{}0[/itex] = 13.7 ft

And the total distance is x = 392 ft

When I plug these variables in...I get something other than 115 ft/s which is the correct answer.

I appreciate your help.

Last edited: