Question

The acceleration of $A$ is as shown in the figure. If the system starts from rest, find the velocity with which the wedge hits the wall. $A$ is constrained to move only in vertical direction.

• A. $2\text{m/s}$
• B. $2\sqrt{2}\text{m/s}$
• C. $\sqrt{2}\text{m/s}$
• D. $\sqrt{3}\text{m/s}$

Answer 1

The correct option is B $2\sqrt{2}\text{m/s}$

By condition of wedge contrained the displacement, velocity and acceleration along normal to the common interface is same.
$a_A\cos \theta =a_B\sin \theta$
$\Rightarrow a_B=a_A\cot \theta$
$\Rightarrow a_B=a_A$
$\Rightarrow a_B=1{\text{ms}}^{-2}$
Applying 3rd equation of motion for wedge
$v^2=u^2+2a_{B}s$
$v^2=0^2+2\left(1\right)\left(4\right)$
$v=2\sqrt{2}\text{m/s}$