Question
A particle $$P$$ is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle $$Q$$ is released on the from smooth the same inclined position. plane $$P$$ and $$Q$$ collide on the in clined plane after $$t = 4$$ second. The speed of projection of $$P$$ is
A particle $$P$$ is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle $$Q$$ is released on the from smooth the same inclined position. plane $$P$$ and $$Q$$ collide on the in clined plane after $$t = 4$$ second. The speed of projection of $$P$$ is
A.
$$5\,m/s$$
B.
$$10\,m/s$$
C.
$$15\,m/s$$
D.
$$20\,m/s$$
Answer :
$$10\,m/s$$
Solution :
It can be observed from figure that $$P$$ and $$Q$$ shall collide if the initial component of velocity of $$P$$ on inclined plane i.e., along incline $${u_{II}} = 0$$ that is particle is projected perpendicular to incline. Time of flight on an inclined plane of inclination $$\alpha $$ is given by
$$\eqalign{ & T = \frac{{2u\sin \left( {\theta - \alpha } \right)}}{{g\cos \alpha }}, \cr & \Rightarrow 4 = \frac{{2u\sin {{90}^ \circ }}}{{10 \times \frac{1}{2}}} \Rightarrow u = 10\,m/s \cr} $$
It can be observed from figure that $$P$$ and $$Q$$ shall collide if the initial component of velocity of $$P$$ on inclined plane i.e., along incline $${u_{II}} = 0$$ that is particle is projected perpendicular to incline. Time of flight on an inclined plane of inclination $$\alpha $$ is given by
$$\eqalign{ & T = \frac{{2u\sin \left( {\theta - \alpha } \right)}}{{g\cos \alpha }}, \cr & \Rightarrow 4 = \frac{{2u\sin {{90}^ \circ }}}{{10 \times \frac{1}{2}}} \Rightarrow u = 10\,m/s \cr} $$
