Questions: A bat strikes a ball. For these initial and final velocities, at what angle above the x axis is the average force exerted by the bat directed? A. 90° B. 56° C. 0° D. 45° E. 34°

A bat strikes a ball. For these initial and final velocities, at what angle above the x axis is the average force exerted by the bat directed? A. 90° B. 56° C. 0° D. 45° E. 34°
Transcript text: 57. A bat strikes a ball. For these initial and final velocities, at what angle above the $x$ axis is the average force excrted by the bat directed? A. $90^{\circ}$ B. $56^{\circ}$ C. $0^{\circ}$ D. $45^{\circ}$ E. $34^{\circ}$
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Solution

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Solution Steps

Step 1: Analyzing the initial and final velocities

The initial velocity _vi_ is along the x-axis, and the final velocity _vf_ is along the y-axis. The change in velocity Δ_v_ = _vf_ - _vi_. Since _vi_ and _vf_ are perpendicular, the force exerted by the bat has components in both x and y directions.

Step 2: Determining the direction of the force

The force exerted by the bat causes the change in momentum of the ball. The direction of the average force is the same as the direction of the change in momentum, and thus the same as the direction of the change in velocity. Δ_v_ has a negative x component and a positive y component. Therefore Δ_v_ points in a direction between the positive y-axis and the negative x-axis.

Step 3: Finding the angle

Since _vi_ and _vf_ are perpendicular to each other, the angle of Δ_v_ above the x-axis (in the counter-clockwise direction) is 90 degrees. Since we have established the force points towards the second quadrant (between positive y and negative x), it will be 90 degrees from the positive x axis.

Final Answer: The final answer is $\boxed{A}$

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