Question

Which of the following relations about the maximum height H of the three balls from the ground during their motion in air is correct?

A) ${H_A} = {H_C} > {H_B}$
B) ${H_A} > {H_B} = {H_C}$
C) ${H_A} > {H_c} > {H_B}$
D) ${H_A} = {H_B} = {H_C}$

Answer 1

Maximum height depends on the angle of projection, initial velocity and acceleration due to gravity. From the pictorial representation, three cases are depicted: one where the object has just reached the maximum height, second where the object has yet not reached the maximum height and third where the object has passed its maximum height.

Complete step by step solution:
Maximum height can be calculated only if the angle of projection, initial velocity of projection and the acceleration due to gravity is known. In the above representation these three quantities are not given therefore we will assume that their angle of projection and initial velocity is the same.

We know that maximum height is reached when the object is at the center of its projectile motion, that is it has completed half of its motion. From the above diagram we can clearly see that object A has just reached its maximum height. Object C has crossed its maximum height. And object B is yet to attain its maximum height.

Since Object A and C has already attained their maximum height and B is yet to reach its maximum height, we can conclude that maximum height for A and C will be equal and that for B it will be less than that of A and C.

Hence Option (A) is the correct option.

Note: Since the velocities and angle of projection was not given hence we assumed them to be the same. Also if B would have reached its maximum height then the maximum height of all three objects would have been the same. Maximum height is obtained when an object is projected at an angle perpendicular to the ground.