A pitcher throws a baseball with a horizontal velocity of 132 ft/s (90 mph) toward home plate that is approximately 60 ft. away. What is the vertical drop of the ball when it reaches the plate? g = 32 ft/s^2.

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A pitcher throws a baseball with a horizontal velocity of 132 ft/s (90 mph) toward home plate that is approximately 60 ft away. What is the vertical drop of the ball when it reaches the plate? g = 32 ft/s2.

To determine the vertical drop of the ball when it reaches the plate, you need to calculate the time it takes for the ball to travel the horizontal distance and then use that time to find the vertical drop.

Step 1: Calculate the time taken to travel the horizontal distance
Given: Horizontal velocity (Vx) = 132 ft/s
Distance (d) = 60 ft
Since the motion is horizontal, there is no acceleration, so the horizontal velocity remains constant throughout the motion. Therefore, we can use the formula:

Time (t) = Distance (d) / Velocity (Vx)

Substituting the given values:
t = 60 ft / 132 ft/s

Step 2: Calculate the vertical drop
Given: Acceleration due to gravity (g) = 32 ft/s^2
Using the formula of motion for vertical motion:

Vertical displacement (h) = 0.5 * g * t^2

Substituting the values:
h = 0.5 * (32 ft/s^2) * (60 ft / 132 ft/s)^2

Simplifying the equation:
h = 0.5 * 32 ft/s^2 * (0.4545 s)^2
h = 1.8181 ft^2/s^2 * 0.2066 s^2
h = 0.375 ft

Therefore, the vertical drop of the ball when it reaches the plate is approximately 0.375 ft.

To find the vertical drop of the ball when it reaches the plate, we need to calculate the time it takes for the ball to travel horizontally and then use that time to find the distance the ball drops due to gravity.

First, let's calculate the time it takes for the ball to travel horizontally. We can use the formula:

time = distance / velocity

Given that the distance is 60 ft and the velocity is 132 ft/s, we can plug these values into the formula:

time = 60 ft / 132 ft/s ≈ 0.4545 s

Now that we know the time it takes for the ball to travel horizontally, we can find the vertical drop by calculating the distance the ball falls due to gravity. We can use the formula:

distance = 0.5 * gravity * time^2

Given that the gravity is 32 ft/s^2 and the time is 0.4545 s, we can plug these values into the formula:

distance = 0.5 * 32 ft/s^2 * (0.4545 s)^2 ≈ 0.8263 ft

Therefore, the vertical drop of the ball when it reaches the plate is approximately 0.8263 ft.