You are operating a canon that can fire at approaching tanks. The canon can fire a projectile at any angle between 0 and 90 degrees. You wish to hit a tank that is changing position at speed u. It is coning toward you. At what angle should you aim if the tank is horizontal distance D away.
Given that
D= 1000 m u= 10 m/s. speed of projection 200m/s.
我係咁計的..
Let the horizontal displacement of the canon ball be x. Let the angle of projection be y. Let the time of flight be t.
200cosy * t = x ..........1 0 = 200siny * t - 5t^2 ......... 2 10t = 1000-x .......... 3
From 2 , t = 40siny ......... 4
Sub 4 into 1 and 3, 200cosy * 40siny = x .........5 10*40siny = 1000-x .........6