Question

3. How much work must be done to a proton to accelerate it from rest to 0.998c.

 

4. A person on Earth observes a space ship approaching from the right with a velocity of 0.75c and a rocket ship approaching from the left at 0.50c. What is the relative velocity of the two ships as measured by a passenger in each of them?

Answer 1

3.

$$W=\frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2$$

$$W=\frac{938.272\:\rm MeV}{\sqrt{1-0.998^2}}-{938.272\:\rm MeV}\\ =13905\:\rm MeV=2.22*10^{-9}\: J$$

4.

$$V=\frac{v+u}{1+\frac{vu}{c^2}}$$

$$V=\frac{0.75c+0.50c}{1+0.75*0.50}=0.91c$$