Question

A baseball pitcher throws a pitch with an initial velocity of 47.0 m/s, directed horizontally. How far does the ball drop vertically by the time it crosses the plate 18.5 m away?

Answer 1

To calculate the vertical drop of a baseball thrown horizontally, one must use the time it takes to travel to the home plate, 18.5 meters at a velocity of 47.0 m/s, and the formula for vertical displacement due to gravity, 0.5 * g * t^2.

Step-by-step explanation:

To determine how far a baseball drops vertically when thrown horizontally at a speed of 47.0 m/s over a distance of 18.5 m, we must consider the effect of gravity on the baseball as it travels towards the plate. Gravity acts downwards on the baseball at an acceleration of approximately 9.81 m/s2, while the horizontal motion of the ball does not affect its vertical motion.

The time it takes for the baseball to reach the plate can be calculated by dividing the horizontal distance by the horizontal velocity:

Time = Distance / Velocity = 18.5 m / 47.0 m/s

Using the formula for the vertical displacement caused by gravity, which is s = 0.5 * g * t2 (where g is gravitational acceleration and t is time), we can calculate how far the ball falls vertically.

First, calculate the time taken: t = 18.5 m / 47.0 m/s ≈ 0.39 seconds

Then calculate the vertical drop: s = 0.5 * 9.81 m/s2 * (0.39 s)2

The vertical drop will then be the result of this calculation.