Answer:
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
Explanation:
According to the addition of relativistic velocities;
[tex]v = \frac{v_1+v_2}{1+v_1 * \frac{v_2}{c_2}}[/tex]
Let the velocity toward the earth be negative; then
[tex]v_1 = 0.80c\\\\v_2 = -0.50 c\\\\v = \frac{(0.80*c-0.50*c)}{(1-0.80*0.50*\frac{c^2}{c^2})})\\\\\\v = \frac{0.30c}{0.60}\\ \\v = 0.50 c[/tex]
Let the velocity away from the Earth be positive;
Then:
[tex]v_1 = 0.80 c \\\\v_2 = 0.50 c\\\\v = \frac{0.80c + 0.50 c)}{1+0.80*0.50*\frac{c^2}{c^2}}\\ \\v = \frac{1.30 c}{1.40 c}\\\\v = 0.928 c[/tex]
