Question

. One technique used in long jumping is to lower the center of gravity in the second-to-last step of the run up in order to push off for a longer amount of time while on the take-off board (i.e., Penultimate style). In contrast, in traditional long jumping no particular attempt is made to lower the center of gravity. Assume that the vertical aspect of the push begins with no upward velocity in both styles of jumping. Also assume that the average upward force is the same for each style and the time of force application is .15 sec in the traditional style and .20 sec in the penultimate style. Compared to the traditional style, will the upward velocity of the jumper in the penultimate style be: (a) much more (at least double), (b) more, (c) the same, (d) less, and (e) much less (less than half).

And why? Which formula allows you to solve this problem.

Answer 1

I think the upward velocity of the jumper in the penultimate style will be more than the traditional style. Correct option is (b) More

Reason -  The amount of force and the length of time that force is applied to an object will tell us the resulting change in momentum. In our case, the amount of force is fixed in both cases. Obviously, mass of athlete is also fixed so we have

F*dt = d(mv)

where d(mv) is change in monetum, dt is time interval for which force is applied,

so, for a fixed F and m , velocity will be more for greater timer interval. As in penultimate style, force was applied for 0.20 seconds and 0.15 seconds for traditional style, so upward velocity will be more in penultimate style.