A 0.140-kg baseball is thrown with a velocity of 27.1 m/s.It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original
Velocity. How long were the bat and ball in contact?
A) $3.07 \times 10 ^ { - 2 } \mathrm {~s}$
B) $1.79 \times 10 ^ { - 3 } \mathrm {~s}$
C) $4.30 \times 10 ^ { - 3 } \mathrm {~s}$
D) $1.28 \times 10 ^ { - 2 } \mathrm {~s}$

Question

A 0.140-kg baseball is thrown with a velocity of 27.1 m/s.It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original
Velocity. How long were the bat and ball in contact? 
A) $3.07 \times 10 ^ { - 2 } \mathrm {~s}$
B) $1.79 \times 10 ^ { - 3 } \mathrm {~s}$
C) $4.30 \times 10 ^ { - 3 } \mathrm {~s}$
D) $1.28 \times 10 ^ { - 2 } \mathrm {~s}$

Quizplus · Accepted Answer

To find the time of contact between the bat and the ball, we use the impulse-momentum theorem, which states that the impulse on an object is equal to the change in its momentum. The impulse can be calculated as the force applied times the time it was applied, and the change in momentum is the mass of the ball times the change in velocity. The initial velocity of the ball is 27.1 m/s, and the final velocity is -37.0 m/s (negative because it's in the opposite direction). The change in velocity is therefore -37.0 m/s - 27.1 m/s = -64.1 m/s. The change in momentum is then $0.140 \, \text{kg} \times -64.1 \, \text{m/s} = -8.974 \, \text{kg} \cdot \text{m/s}$. Given the force of 5000 N, the time of contact can be found by rearranging the impulse formula: $time = \frac{Impulse}{Force} = \frac{-8.974 \, \text{kg} \cdot \text{m/s}}{5000 \, \text{N}} = -1.79 \times 10^{-3} \, \text{s}$. The negative sign indicates the direction of the impulse opposite to the initial direction of the ball, but for the duration, we consider the absolute value.

A 0140-Kg Baseball Is Thrown with a Velocity of 27 3.07×10−2 s3.07 \times 10 ^ { - 2 } \mathrm {~s}3.07×10−2 s

A 0140-Kg Baseball Is Thrown with a Velocity of 27 $3.07 \times 10 ^ { - 2 } \mathrm {~s}$