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 baseball during the throwing motion, we can use the equation for average acceleration:
average acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 0 m/s since the baseball starts from rest, and the final velocity is 38 m/s. The displacement is 3.5 m.
Now, we need to find the time it takes for the baseball to travel the given displacement. To do this, we can use the equation of motion:
displacement = (initial velocity × time) + (0.5 × acceleration × time^2)
Plugging in the given values, we have:
3.5 m = (0 × time) + (0.5 × acceleration × time^2)
Simplifying this equation, we have:
3.5 m = 0.5 × acceleration × time^2
Now, we can rearrange the equation to solve for time:
time^2 = (2 × 3.5 m) / acceleration
time = sqrt[(2 × 3.5 m) / acceleration]
We can substitute this value of time into the equation for average acceleration to find the answer.
average acceleration = (38 m/s - 0 m/s) / sqrt[(2 × 3.5 m) / acceleration]
Simplifying further, we have:
average acceleration = 38 m/s / sqrt[(2 × 3.5 m) / acceleration]
Now, you can input the values and solve for the average acceleration.