A baseball leaves the bat with a speed of 43 m/s and an angle of 45° above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 136 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) 44 m
B) 32 m
C) 34 m
D) 34 m..
E) 34 m.

Question

A baseball leaves the bat with a speed of 43 m/s and an angle of 45° above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 136 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) 44 m
B) 32 m
C) 34 m
D) 34 m..
E) ​34 m.

Quizplus · Accepted Answer

Firstly, we need to find out the time of flight of the ball, which can be calculated using the formula:
time = 2 * (velocity * sin(angle)) / g
where g is the acceleration due to gravity (9.8 m/s^2) and angle is given as 45 degrees.

Plugging in the values, we get:
time = 2 * (43 * sin(45)) / 9.8 = 4.41 seconds (approx.)

Now, we need to find out the horizontal distance covered by the ball in this time, which can be calculated using the formula:
distance = velocity * cos(angle) * time

Plugging in the values, we get:
distance = 43 * cos(45) * 4.41 = 136 meters (approx.)

This means the ball just reaches the fence. However, we need to find how much it clears the fence by.

To do this, we need to find the vertical distance covered by the ball in this time, which can be calculated using the formula:
height = initial height + (velocity * sin(angle) * time) - (0.5 * g * time^2)
where initial height is given as 1 meter.

Plugging in the values, we get:
height = 1 + (43 * sin(45) * 4.41) - (0.5 * 9.8 * 4.41^2) = 34.06 meters (approx.)

Therefore, the ball clears the fence by approximately 34 meters. Hence, the answer is (C).

A Baseball Leaves the Bat with a Speed of 43