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?

Height of cliff is 66.43 meter.

Explanation:

Consider the horizontal motion of shell,

We have equation of motion s = ut + 0.5 at²

Initial velocity, u = 1770 m/s

Acceleration, a = 0 m/s²

Displacement, s = 6520 m

Substituting

s = ut + 0.5 at²

6520 = 1770 x t + 0.5 x 0 xt²

t = 3.68 s

Time of flight of shell = 3.68 s.

Now consider the vertical motion of shell,

We have equation of motion s = ut + 0.5 at²

Initial velocity, u = 0 m/s

Acceleration, a = 9.81 m/s²

Time, t = 3.68 s

Substituting

s = ut + 0.5 at²

s = 0 x 3.68 + 0.5 x 9.81 x 3.68²

s = 66.43 m

Height of cliff is 66.43 meter.