Question

A ship is flying away from Earth at 0.9c (where c is the speed of light). A missile is fired that moves toward the Earth at a speed of 0.5c relative to the ship. How fast does the missile move relative to the Earth

Answer 1

Answer:

the required speed with which the missile move relative to the Earth is -0.727c

Explanation:

Given the data in the question;

relative velocity relation;

u' = u-v / 1 - $\frac{uv}{c^2}$

so let V$_B$ represent the velocity as seen by an external reference frame; u=V$_B$

and let V$_A$ represent the speed of the secondary reference frame; v=V$_A$

hence, u' is the speed of B as seen by A

so

u' = V$_B$-V$_A$ / 1 - $\frac{V_BV_A}{c^2}$

now, given that; V$_A$ = 0.9c  and V$_B$  = 0.5c

we substitute

u' = ( 0.5c - 0.9c ) / 1 - $\frac{(0.5c)(0.9c)}{c^2}$

u' = ( 0.5c - 0.9c ) / 1 - $\frac{c^2(0.5)(0.9)}{c^2}$

u' = ( 0.5c - 0.9c ) / 1 - (0.5 × 0.9)

u' = ( -0.4c ) / 1 - 0.45

u' = -0.4c / 0.55

u' = -0.727c

Therefore, the required speed with which the missile move relative to the Earth is -0.727c