Two objects are projected with same velocity u however at different...

Given: $\alpha + \beta = 90 °$

Range of the first projectile:

${R}_{1} = \dfrac{{u}^{2}\sin 2\alpha}{g}$

Range of the second projectile:

${R}_{2} = \dfrac{{u}^{2}\sin 2\beta}{g} = \dfrac{{u}^{2}\sin ( 180 ° - 2\alpha )}{g} = \dfrac{{u}^{2}\sin 2\alpha}{g}$

As we can see, both are equal.

${R}_{1} = {R}_{2}$

Therefore,

${R}_{1}: {R}_{2} = 1: 1$