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

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.