Two stones are thrown vertically upwards simultaneously with their initial velocities u and u respectively. Prove that the heights reached by them would be in the ratio of : (Assume upward acceleration is –g and downward acceleration to be +g).

Question

Two stones are thrown vertically upwards simultaneously with their initial velocities u and u respectively. Prove that the heights reached by them would be in the ratio of : (Assume upward acceleration is &#x2013;g and downward acceleration to be +g).

Philoid · Accepted Answer

We know for upward motion,

v²= u² - 2gh

so,

h=v² -u²/2g

Highest point v=0

so,

H=u²/2g

Height for first ball, h₁= u₁²/2g

Height for second ball, h₂= u₂²/2g

Then, h₁/h₂= (u₁²/2g) /(u₂²/2g)

= u₁²/u₂²

= h₁:h₂

=u₁²: u₂² Proved