The same force is applied to two skateboards. one rolls across the room and the other moves a few feet and comes to a stop. where was there more work done?

Work done will be more in the case where it moves a few feet and comes to a stop.

Explanation:

When we apply some force on the skateboard to give it velocity then net work done on the skateboard is given as

here we know that

= work done by us to move the skate board

= work done against friction

since here in both cases we applied same force on both skateboards but in first case the change in kinetic energy is small as it is moving across the room while in other case the change will be more as it stops after some distance

so here work done will be more in other case where skateboard will stop after some distance

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft