Two large rigid vertical walls A and B are parallel to each other and separated by `10m`. A particle of mass `10g` is projected with an initial velocity of `20m//s` at `45^@` to the horizontal from point P on the ground, such that `AP=5m`. The plane of motion of the particle is vertical and perpendicular to the walls. Assuming that all the collisions are perfectly elastic, find the maximum height attained by the particle and the total number of collisions suffered by the particle with the walls before it hits ground. Take `g=10m//s^2`.

Options

A. 10 m, 4
B. 20 m, 4
C. 10 m, 5
D. 30 m, 6

Answer

A

Explanation

As the collisions are perfectly elastic, collsion of the ball will not affect the vertical component of its velocity while the horizontal component will be simply reserved.
Hence, `H_(max)=(v_y^2)/(2g)=([20xxsin45^@]^2)/(2xx10)=10m`
Total time of flight
`T=(2v_y)/(g)=(2xx20xx(1/sqrt2))/(10)=2sqrt2s`
Total horizontal distance travelled before striking the ground `x=v_xT=40m`
`PB+BA+AB+BA+AB=45m`
Hence, total number of collision suffered by the particle with the walls before it hits ground `=4`.