(i) Prove that if we use the addition formula, the combined velocity never exceeds the speed of light. Hint: compute cu and show c-u > 0 with the help of c> v and c> u'. (ii) Show that if we obtain u = c, one of two velocities must be c. These two observations show that by combining velocities less than c, we can not even reach the speed of light. Let us consider a multi-stage rocket such that each engine is powerful enough to obtain -30 percent of the speed of light - as the final speed relative to its previous stage. (iii) Let up= 0 be the speed of the stationary launch site, and u = be the speed of the first stage. Use the above addition formula iteratively, show U2, u3 and u4, using rational numbers. (iv) (Optional) Find the smallest stage to obtain more than 90 percent of the speed of light. What if 99 percent?