A particle is projected from a horizontal floor with speed `10(m)/(s)` at an angle `30^@` with the floor and striking the floor after sometime. State which is correct.

Options

A. Velocity of particle will be perpendicular to initial direction two seconds after projection.
B. Minimum speed of particle will be `5sqrt3(m)/(sec)`.
C. Displacement of particle after half second will be `(1)/(4)sqrt(235)`m
D. The particle will strike the floor at 2 sec.

Answer

B, C

Explanation

Min. speed`=10cos30^@=5sqrt3`
`(R )/(2)=(u^2sin60^@)/(2g)=(5sqrt3)/(2)`
`H=(u^2sin^230^@)/(2g)=(5)/(4)`
Displacement`=sqrt(H^2+R^2)=sqrt((75)/(4)+(25)/(16))=(1)/(4)sqrt(325)`
`v_y(2sec)`
`=10sin30^@-10xx2`
`v_y=-15(m)/(s)`
`T=(2usintheta)/(g)=1`sec
Thus, before 2 sec particle will strike the floor.