Question

A baseball is moving at a speed of 2.2 m/s when it strikes the catcher's glove. The padding of the glove is compressed by 2.4 mm before the ball comes to a stop. We want to find the average acceleration of the baseball while it is compressing the glove.

which kinematic formula would be most useful to solve for the target unknown?

Answer 1

To calculate the average acceleration of a baseball compressing a catcher's glove, use the kinematic equation vf2 = vi2 + 2aΔx and solve for acceleration.

Step-by-step explanation:

Finding the Average Acceleration of a Baseball

To determine the average acceleration of the baseball while it is compressing the glove, you need to use a kinematic equation that relates initial velocity, final velocity, acceleration, and distance. One such formula is:

vf2 = vi2 + 2aΔx

Where:

• vf is the final velocity (which is 0 m/s since the ball comes to a stop)
• vi is the initial velocity of the baseball (2.2 m/s)
• a is the average acceleration (what we are solving for)
• Δx is the displacement (2.4 mm, which must be converted to meters)

By rearranging the formula to solve for acceleration, we get:

a = rac{vf2 - vi2}{2Δx}

Plugging in the values:

a = rac{0 - (2.2 m/s)2}{2(0.0024 m)}

After performing the calculations, you'll find the average acceleration of the baseball.