Question

$O{O}^{{}^{\prime }}$ and $A{A}^{{}^{\prime }}$ are two vertical walls. A particle is projected from $O$ with speed $10m/s$ at an angle ${15}^0$ from the horizontal. All collisions with each walls are perfectly elastic. Then choose the correct statement(s).

• A. The horizontal component of velocity will change after each collision.
• B. Particle will land on the ground between points $O$ and $A$.
• C. The total number of collisions with walls is $9$ till particle reaches ground again for the first time after projection.
• D. Time taken by particle to reach the ground is $2\sin {15}^{\circ }$ seconds.

Answer 1

Answer: (A), (C), (D)

Time taken by particle to reach the ground is $2\sin {15}^{\circ }$ seconds.

$A,C,D$

After each collision, horizontal component of velocity will reverse in each collision.
Horizontal range of projectile is $R=\frac{u^2\sin 2\theta }{g}=5\text{m}$
But the distance between both the wall is $0.5\text{m}$.
The distance between two consecutive collision is $0.5\text{m}$ and the horizontal range is obtained $5\text{m}.$ So, the number of collisions are $9$.
Time of flight in projectile is given by:
$T=\frac{2u\sin \theta }{g}=2\sin {15}^{\circ }$