Question

A small ball is projected up a smooth inclined plane with an initial speed of $10m/s$ along the direction at ${30}^o$ to the bottom edge of the slope. It returns to the edge after $2s$. The ball is in contact with the inclined plane throughout the process. What is the inclination angle of the plane ?

• A. ${15}^o$
• B. ${60}^o$
• C. ${37}^o$
• D. ${30}^o$

Answer 1

The correct option is D ${30}^o$

The velocity of the projection of the ball on the inclined force $u=10m/s$

The angle of edge of projection with the ball on edge of the slope $\alpha =30$

The effective acceleration due to gravity towards the bottom edge will be $g\sin \theta$ considering the angle of inclination of the slope is $\theta$ and acceleration due to gravity $g=10m/s^2$

The net displacement of the ball along the normal to the bottom edge of the inclined plane during its motion not $t=2$ sec on the inclined force is $=$ zero

Hence by applying equation of the kinematics we can write

$\theta =O=u\sin {30}^0\times t-\frac{1}{2}g\sin \theta \times t^2$

or, $O=10\sin {30}^0\times 2-\frac{1}{2}\times 10\times \sin \theta \times 2^2$

or, $\sin \theta =\sin {30}^0$

or, $\theta ={30}^0$.