Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be :

Solution

Physics sir · 3 steps

Same launch speed means the range depends only on sin 2θ, so just compare the two sines.

1. Range formula. On flat ground a projectile launched with speed u at angle θ lands at a distance given by the range formula below.

   R = (u² sin 2θ)/g

2. Take the ratio. Both projectiles have the same u and the same g, so these cancel. That leaves R₁/R₂ = (sin 90°)/(sin 60°) = 1/(√3/2) = 2/√3.
3. So. The ranges are in the ratio 2 : √3, which is option (c). The 45° throw goes farther, as it should, because 45° gives the maximum range.

The idea to keep. For equal launch speeds on level ground, range goes as sin 2θ. Double the angle first, then take the sine, and the speed never enters the ratio.

Answer from the NTA final answer key. Solution by PrepWiser.