Two particles `A and B` are projected from the same point in different directions in such a manner that vertical components of their initial velocities are same (Fig. 5.8). Find the ratio of range.
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Explanation

We know that the range of projectile,
`R = (u^2 sin 2 theta)/(g) = ((2 u sin theta))/(g) xx u cos theta = (2 u_x . u_y)/(g)`
As `(u_y)_1 = (u_y)_2 rArr u_A sin theta_A = u_B sin theta_B`
or `(u_A)/(u_B) = (sin theta_B)/(sin theta_A)`
`(R_A)/(R_B) = (2(u_A sin theta_A) (u_A cos theta_A)//g)/(2(u_B sin theta_B)(u_B cos theta_B)//g)`
=`[(u_A cos theta_A)/(u_B cos theta_B)]`
=`(sin theta_B cos theta_A)/(sin theta_A cos theta_B) = (tan theta_B)/(tan theta_A)`.