Question

what would dr. hewitt need to have done to exert an even greater force than he did in his karate demonstration? view available hint(s)
increase the change in momentum, and increase the time duration.
increase the change in momentum, and decrease the time duration.
decrease the change in momentum, and increase the time duration.
decrease the change in momentum, and increase the time duration.
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Explanation:

To determine how to exert a greater force, we use the impulse - momentum theorem, which states that the impulse \( J \) (force \( F \) multiplied by time \( t \), \( J = F\times t \)) is equal to the change in momentum \( \Delta p \), so \( F=\frac{\Delta p}{t} \). To increase the force \( F \), we can either increase the numerator (\( \Delta p \)) or decrease the denominator (\( t \)) (or both).

• For the first option: Increasing \( \Delta p \) and increasing \( t \) would not necessarily increase \( F \), because if \( t \) increases while \( \Delta p \) increases, the effect on \( F=\frac{\Delta p}{t} \) is not clear - cut. It could increase, decrease, or stay the same depending on the rate of change.
• For the second option: Increasing \( \Delta p \) (numerator) and decreasing \( t \) (denominator) will definitely increase \( F \) according to \( F = \frac{\Delta p}{t} \), since a larger numerator and a smaller denominator will result in a larger quotient.
• For the third and fourth options (note: there is a typo in the fourth option, but assuming it's similar to the third): Decreasing \( \Delta p \) and increasing \( t \) will decrease \( F \), because a smaller numerator and a larger denominator will result in a smaller quotient.

Answer:

B. Increase the change in momentum, and decrease the time duration.