Answer to Question #4709 in Mechanics | Relativity for Chris Cook

Question

The muzzle velocity of an armor-piercing round fired from an M1A1 tank is 1770 m/s (nearly 4000 mph or mach 5.2). A tank is at the top of a cliff and fires a shell horizontally. If the shell lands 6520 m from the base of the cliff, how high is the cliff?

Answer 1

Let's sign V = 1770 m/s and L = 6520 m.
The time of a flight is T = L/V. So, the height of a cliff is

H = (gT^2)/2 = (g(L/V)^2)/2 = (9.8(6520/1770)^2)/2 = 66,5 m