Question

A stone is dropped from the top of a tower of height 50 m. At the same time another stone is thrown vertically upwards from the ground with velocity of 20 ms^-1. At what time both stones will cross each other?

Answer 1

Given h = h₁ + h₂

∴ h₁ + h₂ = 50 m

Suppose both the stones cross each other at time 't'
For falling stone

u = 0, a = g

∴ h₁ = 0 + \(\frac{1}{2}\) gt²

h₁ = \(\frac{1}{2}\) gt²

For stone which is thrown vertically upwards,

u = 20 ms^-1, a = -g

∴ h₂ = 20t - \(\frac{1}{2}\) gt²

∴ h₁ + h₂ =   \(\frac{1}{2}\) gt² + 20t - \(\frac{1}{2}\) gt²

or 50 = 20t

∴ t = \(\frac{50}{20}\) = 2.5 s

Based on accelerated motion