# 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

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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