Question

A gun can fire shells with maximum speed v_o and the maximum horizontal range that can be achieved is R = v_o²

If a target farther away by distance Dx (beyond R) has to be hit with the same gun (Fig 4.5), show that it could be achieved by raising the gun t o a height a t least 

h = Δx [1 + Δx/R]

Answer 1

(Hint : This problem can be approached in two different ways:

(i) Refer to the diagram: target T is at horizontal distance x = R + Δx and below point of projection y = – h.

(ii) From point P in the diagram: Projection at speed v_o at an angle θ below horizontal with height h and horizontal range Δx.)