# Question #19fce

Mar 27, 2017

Let the block of mass $m$ be projected along the smooth inclined plane having angle of inclination $\alpha$ with the horizontal and it moves distance $s$ along the inclined plane in time t. During this time if it achieves a vertical height h,then $h = s \sin \alpha$

Now retardation of the block along the inclined plane is $g \sin \alpha$

So $s = v t - \frac{1}{2} g \sin \alpha {t}^{2}$

And

$h = s \sin \alpha$

$\implies h = v \sin \alpha t - \frac{1}{2} g {\sin}^{2} \alpha {t}^{2}$

So potential enrgy of the block at time t will be

${E}_{p} \left(t\right) = m g h$

$= v m g \sin \alpha t - \frac{1}{2} m {g}^{2} {\sin}^{2} \alpha {t}^{2}$

$= a t - b {t}^{2}$

Where $a \mathmr{and} b$ are constants as $v , m , g \mathmr{and} \alpha$ are constants.
So a plot of ${E}_{p} \left(t\right)$ v/s $t$ will be a parabola for the upward and downward movement of the block along the inclined plane.

So option (1) will be the answer.