Question 122: Laws of Motion

Question

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2
 where v is its speed. The maximum height attained by the ball is :

Accepted Answer

F
net
= ma
$$ \Rightarrow $$ -mg - mkv
2
= $$mv{{dv} \over {ds}}$$
$$ \Rightarrow $$ $$ds = {{ - vdv} \over {g + k{v^2}}}$$
$$ \Rightarrow $$ $$\int\limits_{s = 0}^{{H_{\max }}} {ds}  = \int\limits_{v = u}^{v = 0} {{{ - vdv} \over {g + k{v^2}}}} $$
$$ \Rightarrow $$ H
max
= $${1 \over {2k}}\ln \left( {{{g + k{u^2}} \over g}} \right)$$ = $${1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)$$

Answer

$${1 \over k}{	an ^{ - 1}}{{k{u^2}} \over {2g}}$$

Answer

$${1 \over {2k}}{	an ^{ - 1}}{{k{u^2}} \over g}$$

Answer

$${1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)$$

Answer

$${1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)$$

Laws of Motion

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is :

Choose the correct answer: