A fighter jet locks on to a target at 1km and fires a missil

A fighter jet locks on to a target at 1km and fires a missile at 400 m/s with a maximum range of 16km. The target suddenly accelerates and manages to get outside the range of the missile. What is the minimum possible average velocity of the target after the missile is fired

Solution

Given Data :-

Velocity = 400 m/s

Maximum range of missile = 16 km = 16000 m

Now..The time required to complete the range of missile,

time = distance / velocity

t = 16000 / 400

t = 40 s

Now..target suddenly accelerates after the missile is fired..

Thus, the target has covered minimum 15.5 km distance in less than 40 seconds

Thus we take minimum 35 s required to covered the 15.5 km ( outside the range of the missile)

Now, the Minimum possible average velocity of the target after the misssile is fired

V = distance / time

V = 15500 m / 35 s

V = 442.8 m / s

Thus the Minimum Possible Average velocity of the target after the missile fired is V = 442 m/s.