A baseball player hits a baseball (m=0.14 kg) as shown in...

A baseball player hits a baseball $(m=0.14 \mathrm{kg})$ as shown in Figure $\mathrm{P} 7.11 .$ The ball is initially traveling horizontally with a speed of $40 \mathrm{m} / \mathrm{s}$. The batter hits a fly ball as shown, with speed $v_{f}=55 \mathrm{m} / \mathrm{s}.$ a. What are the magnitude and direction of the impulse imparted to the ball? b. If the ball and bat are in contact for a time of $8.0 \mathrm{ms}$, what is the magnitude of the average force of the bat on the ball? Compare this answer to the weight of the ball. c. What is the impulse imparted to the bat?

A baseball player hits a baseball $(m=0.14 \mathrm{kg})$ as shown in Figure $\mathrm{P} 7.11 .$ The ball is initially traveling horizontally with a speed of $40 \mathrm{m} / \mathrm{s}$. The batter hits a fly ball as shown, with speed $v_{f}=55 \mathrm{m} / \mathrm{s}.$
a. What are the magnitude and direction of the impulse imparted to the ball?
b. If the ball and bat are in contact for a time of $8.0 \mathrm{ms}$, what is the magnitude of the average force of the bat on the ball? Compare this answer to the weight of the ball.
c. What is the impulse imparted to the bat?

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Key Concepts

Average Force

The average force during an interaction is obtained by dividing the total impulse imparted to an object by the time interval over which the force was applied. This concept simplifies the analysis of forces that may vary over time by providing a single representative force, especially in short-duration events such as collisions.

Momentum

Momentum is a measure of the motion of an object, defined as the product of its mass and its velocity. Being a vector quantity, momentum carries both magnitude and direction. It is crucial in understanding and predicting how objects behave during interactions and collisions, as changes in momentum reflect the effects of applied forces.

Impulse

Impulse is a vector quantity equal to the change in momentum of an object. It is determined by multiplying the applied force by the duration of time the force is in action, which means that it takes into account both the magnitude and the direction of the force. This concept is especially useful in analyzing situations such as collisions and impacts where forces act over brief time intervals.

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