# Calculating acceleration of gravity on a planet

• mia_material_x1
In summary, an astronaut on a strange planet can jump a maximum horizontal distance of 30m with an initial speed of 9m/s. To find the acceleration of gravity on the planet, the formula Vf^2=Vi^2+2a(Xf-Xi) was used with Vf=0m/s, Vi=9m/s, and X=Xf-Xi=30m, resulting in an acceleration of -1.35m/s^2. However, this calculation may not be entirely accurate as it does not take into account the 2D nature of the jump. An alternative approach would be to use the Range Equation to determine the optimum launch angle for maximizing the range of a projectile.
mia_material_x1

## Homework Statement

An astronaut on a strange planet finds that he can jump a maximum horizontal distance of 30m if his initial speed is 9m/s. What is the acceleration of gravity on the planet?

## Homework Equations

Vf^2=Vi^2+2a(Xf-Xi)

## The Attempt at a Solution

I used the formula mentioned above, plugged in number
Vf=0m/s
Vi=9m/s
X=Xf-Xi=30m
and get a=-1.35m/s^2

I'm not sure if it is correct, could someone double check and tell me if I did anything wrong? Thanks

Consider the trajectory of the jump: It's not a one-dimensional linear motion but rather a 2D curve, one with both horizontal and vertical components. The kinematic equation that you've chosen applies to motion in one dimension and doesn't take into account splitting the given velocity into components.

What's the optimum launch angle to maximize the range of a projectile? Have you covered the Range Equation in your classes? (If not you might want to look it up and try to remember it; it can really come in handy to avoid re-deriving the range of a projectile every time).

mia_material_x1

## 1. What is the formula for calculating acceleration of gravity on a planet?

The formula for calculating acceleration of gravity on a planet is a = GM/r², where a is the acceleration of gravity, G is the universal gravitational constant, M is the mass of the planet, and r is the distance between the planet's center and the object being affected by gravity.

## 2. How does the mass of a planet affect its acceleration of gravity?

The greater the mass of a planet, the greater its acceleration of gravity will be. This is because a larger mass will result in a stronger gravitational pull on objects near its surface.

## 3. What is the unit of measurement for acceleration of gravity?

The unit of measurement for acceleration of gravity is meters per second squared (m/s²).

## 4. How does the distance from a planet's center affect its acceleration of gravity?

The closer an object is to a planet's center, the greater the acceleration of gravity it will experience. This is because the force of gravity decreases as the distance between two objects increases.

## 5. Can the acceleration of gravity on a planet change over time?

Yes, the acceleration of gravity on a planet can change over time due to changes in the planet's mass or distance from other objects, such as stars or moons. However, these changes are usually very small and not noticeable on a human timescale.

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