Question

A particle is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth inclined plane from the same position. P and Q collide on the inclined plane after t= 4 second. The speed of projection of P is

• A. $5\frac{m}{s}$
• B. $10\frac{m}{s}$
• C. $15\frac{m}{s}$
• D. $20\frac{m}{s}$

Answer 1

The correct option is B

$10\frac{m}{s}$

So when ball comes back then

$S_y=0$ (Displacement along y = 0)

$u_y=u$

$a_y=-gcos{60}^{\circ }$

$\Rightarrow 0=ut-\frac{1}{2}g\frac{1}{2}{t}^2$

$\Rightarrow t=\frac{2u}{gcos{60}^{\circ }}$

Its given the collision happens after 4 seconds

$\Rightarrow$ the ball P should come back after 4 second

$\Rightarrow t=\frac{2u}{gcos{60}^{\circ }}=4$

$\Rightarrow u=10\frac{m}{s}$