Question

When a particle is thrown vertically upwards ,its velocity at one third of its maximum height is 10√2 .The maximum height attained by it is

Answer 1

Let's maximum height = H
given height = h = H/3
speed at h = 10√2

now, applying conservation of energy

total energy at h = total energy at H

=> mgh + 0.5 mv^2 = mgH + 0
=> H =
$\frac{3 {v}^{2} }{4g} = 15m$