Question

A rock hits soft mud at a certain speed and penetrates to a certain depth before coming to rest. if you wanted the stone to penetrate four times as far, it would have to hit the mud at what speed? 1. four times as fast. 2. twice as fast. 3. none of the above. 4. five times as fast. 5. six times as fast. 6. three times as fast

Answer 1

in this scenario a rock is hitting a soft mud. so the mud applies an amount of force to decelerate the rock. the general formula for force F=1/2mv². the distance traveled by the rock is d then the average speed(Favg) can be found by dividing force by the distance. Favg= F/d ie Favg=(1/2mv²)/d. now rock need to travel four times deeper then d=4d. now apply the same in the previous formula. Favg=(1/2mv²)/4d 4d=2v so the speed should be doubled to make the stone to penetrate four times