Question

Lift A is going up with velocity 20 m/s and acceleration as $8m/s^2$ in the downward direction. While lift B is going down with 10 m/s and acceleration of $+2m/s^2$ in upward direction. At this moment a bolt in the ceiling of lift A gets loose and falls. Height of the lift is 16 m.

What is the velocity of bolt relative to lift B when it hits the floor of A.?

• A. 18 m/s
• B. 20 m/s
• C. 22 m/s
• D. None of these

Answer 1

Answer: (A)

$\overrightarrow{v_{\frac{b}{a}}}=\overrightarrow{v_b}-\overrightarrow{v_a}$

$\overrightarrow{a_{\frac{b}{a}}}=\overrightarrow{a_b}-\overrightarrow{a_a}=-g-(-8)=-2\frac{m}{s^2}$

$s_{rel}=u_{rel}t+\frac{1}{2}{a}_{rel}{t}^2$

$-16=0+\frac{1}{2}(-2){\left(t\right)}^2$

t=4 sec