A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $m k v ^ { 2 }$ where $v$ is it speed. The maximum height attained by the ball is: (1) $\frac { 1 } { 2 k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { g }$ (2) $\frac { 1 } { k } \ln \left( 1 + \frac { k u ^ { 2 } } { 2 g } \right)$ (3) $\frac { 1 } { k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { 2 g }$ (4) $\frac { 1 } { 2 k } \ln \left( 1 + \frac { k u ^ { 2 } } { g } \right)$
A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $m k v ^ { 2 }$ where $v$ is it speed. The maximum height attained by the ball is:\\
(1) $\frac { 1 } { 2 k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { g }$\\
(2) $\frac { 1 } { k } \ln \left( 1 + \frac { k u ^ { 2 } } { 2 g } \right)$\\
(3) $\frac { 1 } { k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { 2 g }$\\
(4) $\frac { 1 } { 2 k } \ln \left( 1 + \frac { k u ^ { 2 } } { g } \right)$