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

(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 ?

#Physics #HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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

Math	Appears 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}`	$\boxed{123}$

Comments

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).

Francisco Rivera - 8 years 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 ?

Nishant Sharma - 8 years 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).

Francisco Rivera - 8 years ago

Math	Appears 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}`	$\boxed{123}$