Velocity Addition Calculator

Time and space in special relativity experience the same speed of light, because time travels at different rates and distances appear different when moving. Time dilation and length contraction are the two effects. Using our time dilation and length contraction calculators, you can see how they work. The relativistic velocity addition formula is the result of combining these two effects.

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A three-dimensional equation that connects the velocities of objects in various reference frames is known as the velocity-addition formula. Because such formulas apply to successive Lorentz transformations, they can also be used to connect separate frames.

The Relativistic velocity addition formula is as follows: u = (v+w)/(1+(v*w)/c²)

• where, u is the projectile's speed as seen from outside the spaceship
• v is the speed of spaceship
• w is the projectile's speed as seen from within the spaceship
• c is the speed of light (299 792 458 m/s).

Question 1: If a spaceship travelling at half the speed of light approaches the planet, it sends a signal to us via a laser-produced beam of light. As a result, light leaves the ship at 1c, and the spaceship's velocity is 0.6c. Calculate how fast it is approaching the earth.

Solution:

Consider the problem, we have

Space velocity(v)=0.6c

Projectile Velocity(w)=1c

We know that,Relative projectile velocity u = (v + w)/(1 + (v*w)/c²)

u = (0.6+1)/(1 + (0.6*1)/299792458²)

u = 479667932.79999995 / (1 + ( / 8.987551787368176e+16))

u = 299792457.99999994 m/s

Therefore,The spaceship is approaching the earth in 299792457.9999 m/s

1. What is the definition of velocity relativity?

The velocities of an object moving at a relativistic speed are added in relativistic velocity addition. If the source of electromagnetic radiation moves relative to the observer, the viewer perceives relativistic Doppler effects.

2. What is the formula for relativistic velocity addition?

By substituting the spaceship velocity and projectile velocity details in the formula, relative velocity addition can be calculated. Get the answer by solving the equation.

3. What is the velocity of two objects in relation to each other?

The rate at which one object's relative position changes with regard to another is referred to as relative velocity. When two objects are travelling in the same direction, the magnitude of one object's relative velocity with respect to the other is equal to the magnitude difference between the two velocities.