Question

A rock is thrown vertically upward with initial speed $v_0$. Assume constant retardation is proportional to $-v$, acts on rock due to air friction, where $v$ is the velocity of the rock, and neglect the buoyant force exerted by air. Which of the following options is correct? (Given acceleration due to gravity $=g$)

• A. The acceleration of the rock is always equal to $g$.
• B. The acceleration of the rock is equal to $g$ only at the top of the flight.
• C. The acceleration of the rock is always less than $g$.
• D. The speed of the rock upon return to its starting point is $v_0$.
• E. The rock can attain a terminal speed greater than $v_0$ before it returns to its starting point.

Answer 1

Answer: (B)

The acceleration of the rock is equal to $g$ only at the top of the flight.

There are two forces acting on the rock. Gravitational force and the frictional force(proportional to v). Thus the acceleration is affected by the velocity of the particle and the acceleration of the particle would be equal to g only when the velocity is zero i.e. at the topmost point. Thus B is correct.
Also acceleration is different in both the cases(i.e. while ascending and descending) thus initial velocity would be different from the final velocity. Also while descending the air friction force is opposite to the gravitational acceleration force, the terminal velocity cannot be greater than $v_o$