Question

A block slides down an inclined plane of slope $\theta$ with constant velocity. It is then projected up the plane with an initial speed $v_{0}$. How far up the incline will it move before coming to rest?

• A. $\frac{v_{0}^{2}}{4 g \sin \theta}$
• B. $\frac{v_{0}^{2}}{g \sin \theta}$
• C. $\frac{v_{0}^{2}}{2 g \sin \theta}$
• D. $\frac{v_{0}^{2}}{2 g}$

Answer 1

Answer: (A)

$g \sin \theta=\mu g \cos \theta$
$\Rightarrow \mu=\tan \theta$
When block is project up
$a=\sin \theta+\mu g \cos \theta=2 g \sin \theta$
$d _{ stop }=\frac{ v _{0}^{2}}{2 a }=\frac{ v _{0}^{2}}{2 \times 2 g \sin \theta}$
$=\frac{ V _{0}^{2}}{4 g \sin \theta}$