# Distance a particle travels if launched tangentially into space

• aheizler
In summary, the conversation discusses the calculation of the farthest distance a particle, fired off tangentially from the surface of a non-rotating spherical planet with mass M and radius R, will reach from the center of the planet. The equations used in the attempt at a solution include gravitational potential energy and kinetic energy, and conservation of angular momentum is needed when the particle is fired tangentially.
aheizler

## Homework Statement

A non-rotating spherical planet has mass M and radius R. A particle is fired off from the surface with a speed equal to 3/4 the escape speed. Calculate the farthest
distance it reaches (measured from the center of the planet) if it is fired off tangentially.

## Homework Equations

GPE = G*M*m*((1/R) - (1/d))
KE = ½*m*Ve²

## The Attempt at a Solution

I did this problem correctly when the problem stated that the particle is fired off radially (d=R*(16/7)), but I don't know what changes when the particle is fired tangentially.

When fired radially you assume the maximum distance is when the velocity goes to 0. But when fired tangentially (or throwing a ball in the air at an angle), the maximum height doesn't have 0 total velocity (so KE_final is not 0). The maximum height will have 0 radial velocity, but can still have tangential velocity.

So you will need to use conservation of angular momentum to help solve this.

## 1. What is the formula for calculating the distance a particle travels when launched tangentially into space?

The formula for calculating the distance a particle travels when launched tangentially into space is d = v * t, where d is the distance traveled, v is the initial velocity, and t is the time.

## 2. How does the initial velocity affect the distance a particle travels when launched tangentially into space?

The initial velocity has a direct impact on the distance a particle travels when launched tangentially into space. The higher the initial velocity, the farther the particle will travel before being affected by gravity and other forces.

## 3. Can the distance a particle travels when launched tangentially into space be affected by external forces?

Yes, the distance a particle travels can be affected by external forces such as air resistance, gravity, and the presence of other objects in space. These forces can alter the particle's trajectory and ultimately affect the distance it travels.

## 4. Is the distance a particle travels when launched tangentially into space affected by the angle at which it is launched?

Yes, the angle at which a particle is launched can affect the distance it travels. A higher launch angle will result in a longer distance traveled, while a lower launch angle will result in a shorter distance traveled.

## 5. How does the distance a particle travels when launched tangentially into space differ on different planets?

The distance a particle travels when launched tangentially into space can differ on different planets due to variations in gravitational pull and atmospheric conditions. For example, on a planet with a weaker gravitational pull, the particle may travel farther before being pulled back down to the surface.

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