Question

The speed of the block at point C, immediately before it leaves the second incline is

• A. $\sqrt{120}m/s$
• B. $\sqrt{105}m/s$
• C. $\sqrt{90}m/s$
• D. $\sqrt{75}m/s$

Answer 1

Answer: (B)

$\sqrt{105}m/s$

Let us first calculate the velocity at point B immediately after collision.

Just before collision, velocity along plane is $v=\sqrt{2g\left(3\right)}=\sqrt{60}m/s$. Velocity along plane after collision will be $vcos\left({30}^0\right)=\sqrt{45}m/s$.

Now, conserving energy, we get

$\frac{1}{2}m(v_c^2-v_B^2)=mg\left(3\right)$

Solving this equation gives $v_c=\sqrt{105}m/s$