Answer
a. 4.50 GeV.
b. 5.36 GeV/c.
Work Step by Step
a. By the work-energy theorem, the required work is the change in kinetic energy. The initial kinetic energy is 0, so find the final KE.
Find $\gamma$ for this proton.
$$\gamma=\frac{1}{\sqrt{1-v^2/c^2}}=\frac{1}{\sqrt{1-0.985^2}}=5.795$$
The kinetic energy is given by equation 26–5b.
$$KE=(\gamma-1)mc^2=(5.795-1)(938.3MeV)$$
$$=4499.4MeV\approx 4.50GeV$$
That is the work required.
b. The momentum is given by equation 26–4.
$$p=\gamma mv=5.795 (938.3MeV/c^2)(0.985c)$$
$$=5356MeV/c\approx 5.36GeV/c$$