Question

A spaceship moves away from the Earth with a speed of 0.80c. Thespaceship then fires a missile with a speed of 0.50c relative to the spaceship.

Part A

What is the velocity of the missile measured by observers on theEarth if the missile is fired toward the Earth?

Part B

What is the velocity of the missile measured by observers on theEarth if the missile is fired away from the Earth?

Answer 1

the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth = 0.50 c

the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth = 0.928 c

Step-by-step explanation:

According to the addition of relativistic velocities;

`v = (v_1+v_2)/(1+v_1 * (v_2)/(c_2))`

Let the velocity toward the earth be negative; then

`v_1 = 0.80c\\\\v_2 = -0.50 c\\\\v = ((0.80*c-0.50*c))/((1-0.80*0.50*(c^2)/(c^2))))\\\\\\v = (0.30c)/(0.60)\\ \\v = 0.50 c`

Let the velocity away from the Earth be positive;

Then:

`v_1 = 0.80 c \\\\v_2 = 0.50 c\\\\v = (0.80c + 0.50 c))/(1+0.80*0.50*(c^2)/(c^2))\\ \\v = (1.30 c)/(1.40 c)\\\\v = 0.928 c`