What is the apogee altitude of a ballistic missile fired on

What is the apogee altitude of a ballistic missile fired on an optimum trajectory across an 8500 km range? What is the apogee altitude of the missile when fired with the same velocity to a range of 5200 km?

Solution

Apogee is the maximum height attained by the missile during its travel. It is given by the one quarter of the range and solved by the simple projectile motion.

a) apogee = r_max/4 = 8500/4 = 2125 km

b) apogee = 5200/4 = 1300 km

This will be atained when a missile is projected at an angle of 45 deg at which it will attain the maximum range.