One of the fastest recorded pitches in major league...

One of the fastest recorded pitches in major league bascball, thrown by Tim Lincecum in 2009 , was clocked at 101.0 $\mathrm{mi} / \mathrm{h}$ (Fig. P3.8). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 $\mathrm{ft}$ away?

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Key Concepts

Projectile Motion

Projectile motion describes the movement of an object that is launched into the air and then moves under the influence of gravity. In such motion, the horizontal and vertical components are independent. The horizontal component typically remains at a constant velocity (neglecting air resistance) while the vertical component undergoes constant acceleration due to gravity.

Gravitational Acceleration

Gravitational acceleration is the constant rate at which an object accelerates downward, typically approximated as 32.2 ft/s² on Earth in imperial units. This acceleration affects the vertical component of an object’s trajectory, determining how far the object falls over a period of time.

Independent Motion Components

This concept highlights that the horizontal and vertical motions in projectile motion do not affect each other. The time taken to travel a horizontal distance is independent of the object's vertical motion, allowing separate analysis of the two components.

Kinematic Equations in Free Fall

The kinematic equations, particularly the one for displacement under constant acceleration (d = 1/2 g t²), are used to calculate the vertical drop of an object in free fall. These equations are essential for predicting how far an object will fall vertically over a given time interval.

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