a baseball pitcher throws a baseball with a speed of 38m/s. estimate the average acceleration of the ball during the throwing motion,. in throwing the baseball, the pitcher accelerates the ball through a displacement of about 3.5 m from behind the body to hthe point where it is released.
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To estimate the average acceleration of the ball during the throwing motion, we can use the following formula:
Average Acceleration = Change in velocity / Time taken
In this case, the change in velocity is the difference between the final velocity (0 m/s at the point of release) and the initial velocity (38 m/s when the ball is thrown). The time taken would be the time it takes for the pitcher to accelerate the ball through a displacement of 3.5 m.
To find the time taken, we need to know the acceleration. Unfortunately, the problem does not provide us with the acceleration directly. However, we can use the kinematic equation:
Final Velocity² = Initial Velocity² + 2 * Acceleration * Displacement
Since we are interested in the average acceleration, we can rearrange the equation to solve for acceleration:
Acceleration = (Final Velocity² - Initial Velocity²) / (2 * Displacement)
Substituting the known values, we get:
Acceleration = (0 m/s - 38 m/s)² / (2 * 3.5 m)
Simplifying,
Acceleration = (-38 m/s)² / (7 m)
Acceleration = 2,288 m²/s² / 7 m
Acceleration ≈ 327.6 m/s²
Therefore, the estimated average acceleration of the ball during the throwing motion is approximately 327.6 m/s².