Formula That Predicts The Location Of Moving Enemy

A rocket that explodes not on impact, but explodes on a timer will be shot from myself to the enemy. The timer can only be inputted at the start of the shot. The rocket can only go straight and has a speed of 1500m/s . The enemy is moving away from me in a straight line at a speed of 400m/s. The distance between myself and my enemy is 5000m. I need a formula that predicts the precise time until the rocket should explode so that it will explode directly on my enemy’s location.

Solution

v = speed of rocket u = speed of target t = time   They must both arrive at the same place at the same time, with the target having a head start of 5000 m, so   vt = 5000 + ut   1500t = 5000 + 400t   Solve for t (in seconds).