Question

4. A spaceship racing towards Jupiter at 0.70c launches a probe towards the planet at a relative speed of 0.50c. How fast will the probe approach Jupiter as measured by the observer on that planet?

A. 1.4 c

B. -3.3 c

C. 0.89 c

D. 0.78 c

5. An astronaut journeying to the nearby star Alpha Centauat at a speed of 0.99 c relative to the Earth requires 8.57 Earth years to complete hertrip How many years as measured on earth to complete her trip?

A. 1:21 years

B. 60.75 years

C. 5 years

D. 50 years

Answer 1

4.

$$V=\frac{u+v}{1+\frac{uv}{c^2}}=\frac{0.7c+0.5c}{1+\frac{0.35c^2}{c^2}}=0.89c$$

Answer C

5.

$$\Delta t=\frac{\Delta \tau}{\sqrt{1-v^2/c^2}}$$

$$\Delta t=\frac{8.57 \rm\: years}{\sqrt{1-0.99^2}}=60.75\:\rm years$$

Answer B