The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are R₁, R₂ and H₁, H₂ respectively. Choose the correct option :

Solution

Physics sir · 3 steps

42° and 48° add up to 90°, so the ranges match, but the steeper throw always climbs higher.

1. Equal ranges. For the same speed u, the range is R = (u² sin 2θ)/g. Here sin 84° = sin 96°, because sin(180° - x) = sin x. So R₁ = R₂.
2. Unequal heights. The maximum height is H = (u² sin² θ)/2g. Between 0° and 90°, sin θ grows as the angle grows, so the 48° projectile goes higher.

   H₁/H₂ = (sin² 42°)/(sin² 48°) = tan² 42° < 1

3. So. R₁ = R₂ and H₁ < H₂, which is option (b).

The idea to keep. Complementary angles θ and 90° - θ give the same range at the same speed. The larger angle always gives the greater height and the longer time of flight.

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