KVPY SA Exam 2012 Question Paper

A ball falls vertically downward and bounces off a horizontal floor. The speed of the ball just before reaching the floor $\left({\mathit{u}}_1\right)$ is equal to the speed just after leaving contact with the floor $\left({\mathit{u}}_2\right);{\mathit{u}}_1={\mathit{u}}_2$. The corresponding magnitudes of accelerations are denoted respectively by ${\mathit{a}}_1$ and ${\mathit{a}}_2$. The air resistance during motion is proportional to speed and is not negligible. If g is acceleration due to gravity, then