Question

A ball which is at rest is dropped from a height $h$ metre. As it bounces off the floor its speed is $80%$ of what it was just before touching the ground. The ball will then rise to nearly a height :

• A. 0.94 h
• B. 0.80 h
• C. 0.75 h
• D. 0.64 h
• E. 0.50 h

Answer 1

Answer: (D)

$v=\sqrt{2gh}$ ...(1)
After rebounce, ${{v}^{2}}={{u}^{2}}-2gh$
$\Rightarrow$ ${{u}^{2}}={{v}^{2}}+2gh$
$\therefore$ ${{u}^{2}}=2gh'$ ...(2) $\therefore$
$\frac{{{v}^{2}}}{{{u}^{2}}}=\frac{2gh}{2gh}$
$\Rightarrow$ $h'=h\times \frac{{{u}^{2}}}{{{v}^{2}}}=h\times {{\left( \frac{80}{100} \right)}^{2}}$
$=0.64\,h$