A fighter plane is directly over an anti aircraft gun at a time t=0. The plane has a speed of 600km/hr. A shell is fired from an anti aircraft gun at the time t=0, in order to hit the plane. The muzzle velocity V is 1100m/s. Determine the distance the gun should be aimed ahead of the plane in order to hit it if the distance of the plane from the ground is 2500m.

Question

Damon · Answer

the plane and the shell cover the same horizontal distance in time t

T = angle up from horizontal

u = 1100 cos T = 600,000/3600 m/s

so T = 81.3 degrees

so Vi = initial speed up = 1100sin 81.3
= 1087 m/s up

how long to reach 2500 meters high?
2500 = 1087 t - 4.9 t^2

4.9 t^2 + 1087 t - 2500 = 0

solve for t, use + result

d = u t