projectile Motion

Question

A missile is fired with a launch velocity of 15,000 fps at a target 1,200 mi away. At what angle must it be fired to hit the target? How long after it is fired will the target be hit?

Answer 1

r= range = 1200 miles *5280 feet/mile = 6336000 feet = v_xoT (T= time of flight)

rocket reaches peak at T/2 and vy=0 at peak ... thus 0=v_yo-gT/2

vxo=vcos(a) , vyo = vsin(a)... a = launch angle, v=launch velocity = 15000 f/s

Solve system of equations to find a=1/2arcsin(rg/v²) = 8.02degrees