Question 156130
In his second time at bat, the equation h= -.0015d2+ .5d + 4 can be used to model the path of the ball hit by Cecil Fielder. The ball is hit toward the portion of the left field wall that is 347 ft from home plate.

a) The left field wall at Fenway Park is 37 ft high. Did he hit the ball over for a home run? Explain.
:
Using the above equation, assume the ball has to clear the fence, not hit the top of it; 38' when it gets out of park:
-.0015d^2 + .5d + 4 = 38
:
-.0015d^2 + .5d + 4 - 38 = 0
:
-.0015d^2 + .5d - 34 = 0
;
Positive solution is about 238 ft, well within the park
:
If you graphed this, you have good picture of this:
distance on the x axis, ball height on the y axis
you can see it would hit the ground just before the base of the wall at 347 ft
(The wall is probably too high for a ground rule double possibility)
{{{ graph( 300, 200, -100, 400, -30, 70, -.0015x^2+.5x+4) }}}
:
b) Along the the third base line, the wall is 315 ft from home plate. Assume that the angle between the third base line and the wall is a right angle. Find the angle between the third base line and the path of the ball.
:
Side opposite = 37, side adjacent = 315; find angle A
:
Tan(A) = {{{37/315}}}
A = 6.7 degrees