Mechanics Problem

A heavy stone is thrown from a cliff of height h in a given direction. The speed with which it hits the ground

(a) must depend on the speed of projection

(b) must be larger than the speed of projection

(c) must be independent of the speed of projection

(d) may be smaller than the speed of projection

I think answer should be (a) and (d), considering drag force. But surprisingly the answer given is (a) and (b). I don't get the point in (b) being correct. Any idea ?

Note by Nishant Sharma
5 years, 2 months ago

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Well, (a) is clearly right (think of throwing the ball straight down at v and 2v, evidently the final velocity will change)

If we consider conservation of mechanical energy, we see that the initial gravitational potential energy must be converted to kinetic energy. Therefore, the kinetic energy must increase, which means that the speed when it hits the ground must be greater than the speed of projection. Although in real life, some amount of energy will be lost due to air resistance, the fact that it is a heavy stone means that this amount will be insignificant to the problem (drag is negligible).

- 5 years, 1 month ago

Drag force has a general dependence of the form F=(C$$\rho$$A$$v^{2}$$)/2 , I believe. How does this explain your statement of the stone being heavy ?

- 5 years, 1 month ago

You are over-thinking the problem. You simply need to realize that air resistance is negligible because of the nature of the object you are launching (for example, if the problem said a light feather, it would be completely different).

- 5 years, 1 month ago