A particle is projected vertically upwards in a medium that exerts a constant resistive force. It is observed that the time taken by the particle to descend from its maximum height to the point of projection is twice the time taken to ascend. If g is the acceleration due to gravity, the constant deceleration caused by the resistive force is :

Step-by-step solution

Let the constant deceleration due to the resistive force be a_r . During the upward motion, the net acceleration is downwards and its magnitude is a_ up = g + a_r . The maximum height h reached is given by h = 1 2 a_ up t_ up ^2 . During the downward motion, the resistive force acts upwards, so the net downward acceleration is a_ down = g - a_r . The distance covered is the same, so h = 1 2 a_ down t_ down ^2 . Equating the two expressions for h : 1 2 (g + a_r) t_ up ^2 = 1 2 (g - a_r) t_ down ^2 Rearranging the te