Two particles are projected from the same point with the same speed at angles of…

PHYSICS · Multi correct · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two particles are projected from the same point with the same speed

u

at angles of projection

\alpha

and

\beta

and strike the horizontal ground at the same point. If

h_1

and

h_2

are their maximum heights,

R

is their common range, and

t_1

and

t_2

are their times of flight, respectively, then (1)

\alpha+\beta=\frac{\pi}{2}

(2)

R=4\sqrt{h_1h_2}

(3)

\frac{t_1}{t_2}=\tan\alpha

(4)

\tan\alpha=\sqrt{\frac{h_1}{h_2}}