Can you solve this physics problem? \ stacker news ~AskSN

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210 sats \ 7 comments \ @Bell_curve 8 Apr AskSN

@0xbitcoiner @Riberet @Undisciplined @Fundamentals @south_korea_ln @SimpleStacker @cryotosensei @Satosora

103 sats \ 1 reply \ @SimpleStacker 8 Apr

Gravitational potential energy =

U

\frac{GMm}{R}

Escape velocity =

v_{esc}

\sqrt{\frac{2GM}{r}}

Kinetic energy of launch:

 $\begin{align} K_0 &= \frac{1}{2}m(2v_{esc})^2 = \frac{1}{2} m 4v_{esc}^2 \\ &= 2 m v_{esc}^2 = 2m \frac{2GM}{r} \\ &= 4 U \end{align}$

Kinetic energy after launch =

K_0 - U

3U

 $\begin{align} 3U &= 3 \frac{GMm}{r} = \frac{3}{2} \frac{2GM}{r} \\ &= \frac{3}{2} v_{esc}^2 = \frac{1}{2} \left(\sqrt{3}v_{esc}\right)^2 \end{align}$

So the answer is D)

\sqrt{3}v_{esc}

0 sats \ 0 replies \ @Bell_curve OP 8 Apr

Nice job

40 sats \ 1 reply \ @Undisciplined 8 Apr

I didn't remember the escape velocity formula off the top of my head, so the answer is no.

Me plus looking it up would look like what @SimpleStacker did.

50 sats \ 0 replies \ @SimpleStacker 8 Apr

I enjoy solving puzzles like these... I almost wish mathematical econ was more useful in real life so those skills would be more applicable.

10 sats \ 1 reply \ @Fundamentals 8 Apr

I didnt want to get too cute with the answer but there arent a lot of details provided, so I do make some assumptions.

There is gravity on the planet (clearly because it has mass and a given escape velocity)
There is matter in outer space that will have gravity

The speed exceeds the escape velocity so greatly that I will say that the rock will land inside some mass in outer space after which the speed of the rock will be: