Two projectiles A and B are thrown with initial velocities of 40 m s - 1 and 60 m s - 1 at angles 30 ° and 60 ° with the horizontal respectively. The ratio of their ranges respectively is ( g = 10 m s - 2 )

Step-by-step solution

The range R 1 of the first projectile is given by R 1 = u 1 2 sin 2 θ 1 g       . . . ( 1 ) The range R 2 of the second projectile is given by R 2 = u 2 2 sin 2 θ 2 g       . . . ( 2 ) Divide equation (1) by equation (2) and simplify to obtain the ratio of the ranges. R 1 R 2 = u 1 2 sin 2 θ 1 g u 2 2 sin 2 θ 2 g =   u 1 2 sin 2 θ 1 u 2 2 sin 2 θ 2       . . . 3 Substitute the values of the known parameters into equation (3) to calculat