- #1

Icky Fizz

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## Homework Statement

I'm trying to calculate a value for gravity based on a known jump height and time. It's working when the take-off and landing heights are the same but I'm struggling for a solution if the landing point is higher than the take-off. I'm more interested in understanding a solution method than getting an answer to a specific question, so I've used symbols instead of values, thanks.

An astronaut lands on a planet and jumps up to a height of 'S' and lands 'T' seconds later on a rock at height 'R'. What is the value of the planet's gravity?

## Homework Equations

s = ut + 0.5*at

^{2}

v = u + at

## The Attempt at a Solution

When take-off and landing are the same, I use s = ut + 0.5*at

^{2}for the falling time (half total time), with u=0, rearranging s = 0.5*at

^{2}to give an answer a = 2s / (t/2)

^{2}I think this method is fine.

With a height difference, I guess a solution is based on the same equation, but separating the jump into two parts - the initial upward part to reach the rock height on the way up, and then treating the the rest of the jump as before. But I don't seem able to figure out how much time is spent in each part of the jump?