Question

A ball is thrown vertically upwards with a speed u. It comes back to earth and reaches
the point of projection with a speed v. Neglecting air resistance one can conclude that:
(a) u v
(b) u>v
(c) u = v​

Answer 1

OPTION c) IS CORRECT.

Given:

• initial velocity = u
• Final velocity upon reaching ground = v

To find:

Relation between u & v ?

Calculation:

First let's calculate the max height:

${ (v_{1}) }^{2} = {u}^{2} + 2( - g)h$

$\implies {0}^{2} = {u}^{2} - 2gh$

$\implies h = \dfrac{ {u}^{2} }{2g}$

Now, from max height, the starting velocity will be zero. So, final velocity will be :

${v}^{2} = {( u_{h}) }^{2} + 2gh$

$\implies {v}^{2} = {0 }^{2} + 2g( \dfrac{ {u}^{2} }{2g} )$

$\implies {v}^{2} = {u}^{2}$

$\implies \: v = u$

So, option c) is correct.