Question

A baseball is hit at ground level. The ball is observed to reach its maximum height above ground level 3.0 s after being hit. And 2.5 s after reaching this maximum height, the ball is observed to barely clear a fence that is 97.5 m from where it was hit. How high is the fence?

Answer 1

Horizontal:
97.5=vi*5.5
so vihorizontal= 97.5/5.5 m/s

vertical: at the top, the vertical veloicty is zero, so
0=viy-1/2 g*3^3
viy=4.9*9g

so now we have the vertical and horizontla components.

finally
hf=viy^t-1/2 g t^2 so at t=5.5, knowing viy, calculate hf.

Answer 2

5.5

Answer 3

First, you want to find the maximum height.
At the maximum height, you know the velocity must be 0.

vi = initial velocity
vy(t) = vertical velocity
t1 = first time (3 s)

SO:
vy(t1) = -g*t1 + vi*sinθ
0 = -g*t1 + vi*sinθ
vi*sinθ = g*t1

Now, it's just a matter of substituting that into the equation for vertical distance.

ymax = maximum height reached by ball
y(t) = vertical distance

ymax = y(t1) = -1/2*g*t1^2 + vi*sinθ*t1
= -1/2*g*t1^2 + g*t1*t1
= -1/2*g*t1^2 + g*t1^2
= 1/2*g*t1^2
= 1/2(9.8)3^2 = 44.1m

From there, it's a simple matter of finding vi*sinθ.

44.1 = -1/2*g*t1^2 + vi*sinθ*t1
44.1 = -1/2(9.8)3^2 + vi*sinθ(3)
vi*sinθ = 29.4

When t = 5.5
y(5.5) = -1/2(9.8)5^2 + 29.4(5.5)
= 13.475m

Thus, in order for the ball to clear the fence, it must be less than 13.475 m!