Its fuel provides the energy to accelerates the ship to a

Question

A space ship leaves earth with a total mass (including its fuel) = m_i. Its fuel provides the energy to accelerates the ship to a final speed of u; as a result, the ship's final mass m_f = m_i - Δm, where Δm is the mass of the fuel that is converted into kinetic energy.

a) Show that Δm = m_i (γ-1) / γ.

b) What is the value of Δm/m_i if u = 0.5c?

c) What is the value of Δm/m_i if u = 0.99c?