# Free fall acceleration on a planet

• drummerdimitr
In summary, an astronaut on a strange planet can jump a maximum horizontal distance of 15 m with an initial speed of 3 m/s. To determine the free fall acceleration on the planet, the equation R=Vi^2sin2α/g is used, where R is the range, Vi is the initial velocity, and α is the launch angle. By launching the projectile at 45 degrees, the greatest maximum range can be achieved, with a free fall acceleration of 0.6m/s2.
drummerdimitr

## Homework Statement

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15 m if her initial speed is 3 m/s. What is the free fall acceleration on the planet?

R=Vi^2sin2α/g

## The Attempt at a Solution

15=9sin2α/g g=9sin2α/15

Solution:
To have maximum range for a given initial velocity, her launch angle must be q0 = 45o. Her range then is R = (v02sin2q 0)/g' = v02sin90o/g' = v02/g'. We have g' = v02/R = 0.6m/s2.

Source: http://electron9.phys.utk.edu/phys135d/modules/m3/Projectile%20motion.htm

Scroll down to almost at the bottom of the page.

Last edited by a moderator:
Thanks for clarifying things up. I never knew that launching a projectile at 45 degrees would result in the greatest maximum range.

## 1. What is free fall acceleration on a planet?

Free fall acceleration on a planet refers to the rate at which an object falls towards the planet's surface due to the force of gravity. It is a constant value that is determined by the mass and radius of the planet.

## 2. How is free fall acceleration calculated?

Free fall acceleration can be calculated using the formula a = GM/r^2, where G is the universal gravitational constant, M is the mass of the planet, and r is the distance between the object and the center of the planet.

## 3. Is free fall acceleration the same for all objects on a planet?

Yes, free fall acceleration is the same for all objects on a planet, regardless of their mass or size. This is because the acceleration due to gravity is independent of the object's mass.

## 4. How does free fall acceleration vary on different planets?

Free fall acceleration varies on different planets depending on their mass and radius. The larger the planet's mass and radius, the greater the free fall acceleration will be.

## 5. What is the value of free fall acceleration on Earth?

The value of free fall acceleration on Earth is approximately 9.8 m/s^2. This means that for every second an object falls on Earth, its speed increases by 9.8 meters per second.

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