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A 140 g baseball is moving horizontally to the right at 27 m/s when it is hit by the bat. The ball flies off to the left at 55 m/s, at an angle of 25° above the horizontal. What is the change in momentum of the baseball?

1) 0.14 kg·m/s
2) 0.28 kg·m/s
3) 0.42 kg·m/s
4) 0.56 kg·m/s

User Aeronth
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1 Answer

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Final answer:

The change in momentum of the baseball is calculated by taking the difference in the final and initial momenta, leading to a change of -10.759 kg·m/s. The magnitude of this change is 10.759 kg·m/s, which does not match any of the provided options. The options might have been incorrectly written or calculated by the student.

Step-by-step explanation:

The subject of the question is Physics, specifically the topic of momentum and its change during a collision in mechanics. To calculate the change in momentum of the baseball, we must consider both the initial and final velocities and directions of the baseball.

Initially, the baseball has a momentum of p_initial = mass × velocity to the right (we can consider the right direction as positive). The mass of the baseball is 140 g (which is equivalent to 0.14 kg), and the initial velocity is 27 m/s. Therefore, the initial momentum is p_initial = 0.14 kg × 27 m/s = 3.78 kg·m/s to the right.

After being hit, the baseball moves to the left with a velocity component in the horizontal direction. To find this component, we use the cosine of the angle since the velocity vector is at a 25° angle above the horizontal. The horizontal component of the final velocity is v_horizontal = 55 m/s × cos(25°). Plugging in the values, we get v_horizontal ≈ 49.85 m/s. Now we can calculate the final momentum in the horizontal direction as p_final = 0.14 kg × -49.85 m/s = -6.979 kg·m/s (negative since it's to the left).

The change in momentum, Δp, is the difference between the final and initial momenta: Δp = p_final - p_initial. Δp = -6.979 kg·m/s - 3.78 kg·m/s = -10.759 kg·m/s. The magnitude of the change in momentum is 10.759 kg·m/s, which is not one of the options given in the question. The student may have made a mistake while listing the options or while converting units.

User Jtepe
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