Velocity Addition Calculator

The following are the steps to solve the relative projectile velocity of an object.

• Get the spaceship velocity, projectile velocity details.
• Add those velocities and multiply them.
• Divide the product by the square of the speed of the light.
• Add 1 to the result.
• Divide the sum of velocities by the result from above step to obtain the relative projectile velocity.

The sum of the spaceship speed and fired projectile speed is equal to the projectile travelling speed.

The relativistic velocity addition equation is as follows:

u = (v + w) /(1 + (v * w)/c²)

Where,

c is the speed of the light and its value is 299,792,458 m/s

v is the speed of the spaceship

w is the speed of the projectile as seen from the spaceship

u is the speed of the projectile as seen outside of the spaceship

Example

Question: If the spaceship heading directly towards the earth is half of the speed of the light sends a signal to us on alaser-produced beam of light. Given that, the light leaves the ship at a speed c and spaceship velocity is 0.500c. Calculate the speed at whicch it approaches the earth?

Solution:

Given that

Spaceship velocity v = 0.5c

projectile velocity w = c

Relative projectile velocity u = (v + w) /(1 + (v * w)/c²)

u = (0.5c + c) /(1 + (0.5c * c)/c²)

= 1.5c/(1 + 0.5c²/c²

= 1.5c/(1 + 0.5)

= 1.5c/(1.5)

= c

Therefore, the relative projectile speed is c.

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1. What is the formula of relative velocity?

The relativistic velocity addition formula is u = (v + w)(1 + (v x w)/c²). Here, v is the speed of the spaceship, w is the speed of the projectile from the spaceship, u is the speed of the projectile outside of the spaceship.

2. How to find relativistic velocity addition?

Relative velocity addition can be calculated by substituting the spaceship velocity and projectile velocity details in the formula. Solve the equation and get the result.

3. What is the relativity of velocity?

Relativistic velocity addition is the velocities of an object moving at a relativistic speed. An observer of electromagnetic radiation sees relativistic Doppler effects if the source of the radiation is moving relative to the observer.

4. How to use the velocity addition calculator?

A free and user-friendly velocity addition calculator is used to calculate the relative projectile velocity. Enter spaceship velocity, projectile velocity details and hit the calculate button to check the relative projectile velocity as result.