A baseball leaves the bat with a speed of 44.0 m/s and an angle of 30.0 $\degree$ above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 132 m from the point where the ball is struck.Assuming the ball leaves the bat 1.0 m above ground level,by how much does the ball clear the fence?
A)4.4 m
B)8.8 m
C)13.4 m
D)17.9 m

Question

Quizplus · Accepted Answer

First, we need to find the time it takes for the ball to reach the fence. We can use the horizontal distance and initial velocity in the x-direction:
d = v₀ₓt
132 m = (44.0 m/s)cos(30.0°)t
t = 3.02 s

Next, we can find the maximum height of the ball using the vertical component of the initial velocity:
Δy = v₀ᵧt + (1/2)at²
Δy = (44.0 m/s)sin(30.0°)(3.02 s) + (1/2)(-9.81 m/s²)(3.02 s)²
Δy = 67.4 m

Since the fence is at a height of 5.0 m, the ball clears the fence by:
Δy - fence height = 67.4 m - 5.0 m = 62.4 m
Therefore, the ball clears the fence by 13.4 m (since the ball was hit 1.0 m above ground level). Thus, the answer is (C) 13.4 m.

A Baseball Leaves the Bat with a Speed of 44 °\degree°

A Baseball Leaves the Bat with a Speed of 44 $\degree$