Question

Due to air a falling body faces a resistive force proportional to square of velocity $v$, consequently its effective downward acceleration is reduced and is given by $a=g-k{v}^2$ where $k=0.002m^{-1}$. The terminal velocity of the falling body is (in m/s)

• A. $60$
• B. $70$
• C. $80$
• D. $90$

Answer 1

The correct option is B $70$

As velocity increases $a$ will decrease and at some point, it will become zero and velocity become constant that is terminal velocity.

At terminal velocity- $g-k{v}_{ter}^2=0⟹v_{ter}^2=\frac{g}{k}=\frac{9.8}{0.002}=4900⟹v_{ter}=70\frac{m}{s}$