Question

The instant before a batter hits a 0.14-kilogram baseball, the velocity of the ball is 45 meters per second west. The instant after the batter hits the ball, the ball's velocity is 35 meters per second east. The bat and ball are in contact for 1.0 x 10-2 second.
1. find the magnitude and direction of the average acceleration of the baseball while it is in contact with the bat.
2. calculate the magnitude of the average force the Bat exerts on the ball while they are in contact. ​

Answer 1

(1) The magnitude and direction of the average acceleration of the baseball while it is in contact with the bat is 8,000 m/s² east.

(2) The magnitude of the average force the Bat exerts on the ball while they are in contact is 1,120 N.

The given parameters:

• Mass of the baseball, m = 0.14 kg
• Initial velocity of the baseball, u = 45 m/s west (negative direction)
• Final velocity of the baseball, v = 35 m/s east (positive direction)
• Time of contact, t = 0.01 s

The magnitude and direction of the average acceleration of the baseball while it is in contact with the bat is calculated as follows:

$a = \frac{v- u}{t} \\\\a = \frac{35 - (-45)}{0.01} \\\\a = \frac{80}{0.01} \\\\a = 8,000 \ m/s^2$

The magnitude of the average force the Bat exerts on the ball while they are in contact is calculated as follows;

$F = ma\\\\F = 0.14 \times 8,000\\\\F = 1,120 \ N$

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