# Calculating gravity from height and time of a jump

• Icky Fizz
In summary, the problem involves calculating the value of gravity on a planet based on a known jump height and time. When the take-off and landing heights are the same, the equation s = ut + 0.5*at2 can be used, with rearrangement to solve for a. However, when there is a height difference, it may be necessary to separate the jump into two parts and use multiple equations, such as d = Vi*t + 0.5*a*t and V = Vi + a*t, to solve for g. It is important to be careful with signs when using acceleration as -g.
Icky Fizz

## 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?

s = ut + 0.5*at2
v = u + at

## The Attempt at a Solution

When take-off and landing are the same, I use s = ut + 0.5*at2 for the falling time (half total time), with u=0, rearranging s = 0.5*at2 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?

Welcome to PF, Fizz!
Interesting problem! I wrote Vi for the initial upward velocity and t for the time to maximum height so I have 3 unknowns including g. That means 3 equations needed. I'm an old high school teacher so I usually only remember two accelerated motion formulas: d = Vi*t + .5*a*t and V = Vi + a*t.
I used the d one twice for distance R and distance T. And the V one for the maximum height when V = 0. It should be just a matter of eliminating t and Vi to get an answer for g. Be careful about the signs; I took acceleration to be -g so g comes out positive, but you could do it with g negative if you prefer.

Thanks for your suggestion, sounds much simpler than the quadratic equation I ended up with working out how much time was spent going up and how much coming down!

## What is the formula for calculating gravity from height and time of a jump?

The formula for calculating gravity from height and time of a jump is g = (2h / t^2), where g is the acceleration due to gravity in meters per second squared (m/s^2), h is the height of the jump in meters (m), and t is the time of the jump in seconds (s).

## How do you measure the height and time of a jump?

The height of a jump can be measured using a measuring tape or ruler, while the time of the jump can be measured using a stopwatch or timer. The jumper should start the timer as soon as they leave the ground and stop it when they land back on the ground.

## What are the units for calculating gravity from height and time of a jump?

The units for calculating gravity from height and time of a jump are meters per second squared (m/s^2). This unit represents the acceleration due to gravity, which is commonly measured in terms of how fast an object falls towards the ground.

## How does air resistance affect the calculation of gravity from height and time of a jump?

Air resistance can affect the calculation of gravity from height and time of a jump by slightly decreasing the acceleration due to gravity. This is because air resistance creates drag, which can slow down the rate of acceleration. However, for most jumps, air resistance can be considered negligible and does not significantly impact the calculation.

## What factors can influence the accuracy of calculating gravity from height and time of a jump?

The accuracy of calculating gravity from height and time of a jump can be influenced by several factors. These include errors in measurement of height or time, air resistance, and variations in the acceleration due to gravity caused by different locations on Earth. To increase accuracy, multiple measurements and averaging can be used.

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