Question

A small marble is projected with a velocity of $10m/s$ in a direction ${45}^{\circ }$ from the $y-$direction on the smooth inclined plane. Calculate the magnitude of its velocity after $2s$. (Take $g=10m{s}^2$ )

• A. $10m{s}^{-1}$
• B. $5m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $22.3m{s}^{-1}$

Answer 1

The correct option is A $10m{s}^{-1}$

Resolving components along $x$ and $y$ directions of velocity
$u_x=vcos\left(45\right)u_y=vsin\left(45\right)$
acceleration of gravity is along inclination of plane
$a_x=gsin\left(45\right)$
Applying kinematics equation $v=u+at$ the change in velocity along x direction
$v_x=\frac{10}{\sqrt{2}}-\frac{g}{\sqrt{2}}\times 2\Rightarrow v_x=-\frac{g}{\sqrt{2}}$
the velocity along y direction will be constant
$\Rightarrow v_y=\frac{10}{\sqrt{2}}$
The magnitude of velocity $\sqrt{{v_x}^2+{v_y}^2}=10m/s$