A karate master strikes a board with an initial velocity of 18.0 m/s,decreasing to 4.0 m/s as his hand passes through the board.If the time of contact with the board is 0.002 s,and the mass of the coordinated hand and arm is 1.0 kg,what is the force exerted on the board?
A) 11,000 N
B) 0.028 N
C) 0.044 N
D) 7,000 N
E) 9,000 N

Question

A karate master strikes a board with an initial velocity of 18.0 m/s,decreasing to 4.0 m/s as his hand passes through the board.If the time of contact with the board is 0.002 s,and the mass of the coordinated hand and arm is 1.0 kg,what is the force exerted on the board?
A) 11,000 N
B) 0.028 N
C) 0.044 N
D) ​7,000 N
E) ​9,000 N

Quizplus · Accepted Answer

We can use the impulse-momentum theorem to solve this problem. The impulse on the board is equal to the change in momentum of the hand and arm. 
$$
J = \Delta p = m\Delta v = 1.0	ext{ kg}(4.0	ext{ m/s} - 18.0	ext{ m/s}) = -14	ext{ kg m/s}
$$
The negative sign indicates that the momentum of the hand and arm decreases during the collision. The impulse is also equal to the force multiplied by the time of contact:
$$
J = F\Delta t
$$
Rearranging this equation gives
$$
F = \frac{J}{\Delta t} = \frac{-14	ext{ kg m/s}}{0.002	ext{ s}} = -7,000	ext{ N}
$$
The negative sign indicates that the force is directed towards the hand, opposite to the direction of motion. We can ignore the negative sign when reporting the answer, so the force exerted on the board is 7,000 N. Therefore, the best choice is D.

A Karate Master Strikes a Board with an Initial Velocity