8. There is a ball at rest in your reference frame with a mass M. A...
8. There is a ball at rest in your reference frame with a mass M. A second ball also with the rest mass M is moving with speed v. The two balls collide, stick together, and continue on. Keep in mind that the combined mass after the collision will not be 2M.
a. Write out the equation for conservation of relativistic momentum in terms of the initial and final speeds.
b. Write out the equation for conservation of relativistic energy in terms of the initial and final speeds.
c. Use the two equations from a and b to find the final speed of the two balls. (A bit of algebra is required. Remember, the mass of the two balls after the collision, will not be the same as the original two balls. To solve for the new speed you don't necessarily have to solve for the new mass.)
d. from your answer to part c, find the approximate final speed in the limit of v<<c
e. From your answer to part c, find the approximate final speed in the limit of v~c. (~=approximately)
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