A major league pitcher can throw a baseball in excess of 40.8 m/s. if a ball is thrown horizontally at this speed, how much will it drop by the time it reaches the catcher who is 15.4 m away from the point of release?

Question

A major league pitcher can throw a baseball in excess of 40.8 m/s. if a ball is thrown horizontally at this speed, how much will it drop by the time it reaches the catcher who is 15.4 m away from the point of release?

Answer 1

To find the vertical drop of the ball, we need to determine the time it takes for the ball to reach the catcher.

Step 1: Calculate the time of flight (t):
We can use the horizontal distance (d) and the horizontal speed (v) of the ball to calculate the time using the formula: t = d / v.

Given:
Horizontal distance (d) = 15.4 m
Horizontal speed (v) = 40.8 m/s

t = 15.4 m / 40.8 m/s
t ≈ 0.377 s

Now that we have the time of flight, we can calculate the vertical drop (h).

Step 2: Calculate the vertical drop (h):
We can use the formula for the vertical drop of an object in freefall. The equation is:

h = 0.5 * g * t^2

where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time of flight.

h = 0.5 * 9.8 m/s^2 * (0.377 s)^2
h ≈ 0.069 m

Therefore, by the time the ball reaches the catcher, it will drop approximately 0.069 meters.

Answer 2

To determine how much the ball will drop by the time it reaches the catcher, we need to analyze the motion of the ball.

First, we need to determine the time it takes for the ball to travel from the release point to the catcher. We can find the time using the horizontal distance and the horizontal velocity of the ball.

The formula to calculate the time is:

time = distance / velocity

Plugging in the values, we have:

time = 15.4 m / 40.8 m/s

Simplifying the equation, we find:

time ≈ 0.38 seconds

Now, we know the time it takes for the ball to reach the catcher. To calculate the vertical displacement or drop, we can use the equation of motion for vertical motion:

vertical displacement = (0.5 * acceleration due to gravity * time^2)

Since the ball is thrown horizontally, the vertical acceleration due to gravity is the only force acting on it. Neglecting air resistance, we can assume the acceleration due to gravity is approximately 9.8 m/s^2.

Plugging in the values into the equation, we have:

vertical displacement = 0.5 * 9.8 m/s^2 * (0.38 seconds)^2

Simplifying the equation, we get:

vertical displacement ≈ 0.69 meters

Therefore, the ball will drop approximately 0.69 meters by the time it reaches the catcher who is 15.4 meters away from the point of release.