Two balls are projected from the same point in directions `30^@` and `60^@` with respect to the horizontal . What is the ratio of their initial velocities if they have the same range?

Explanation

If the balls have same range , then `R_1=R_2`
i.e., `(u_1^2sin(2times30^@))/g=(u_2^2sin(2times60^@))/g`
`impliesu_1^2sin60^@=u_2^2 sin120^@`
`impliesu_1^2/u_2^2=(sin120^@)/(sin60^@)impliesu_1^2/u_2^2=(cos30^@)/(sin60^@)`
`impliesu_1^2/u_2^2=(sqrt3/2)/(sqrt3/2)or u_1:u_2=1:1`