Two objects are projected with same velocity 'u' however at different angles α and β with the horizontal. If α+β=90°, the ratio of horizontal range of the first object to the 2nd object will be :

Solution

Physics sir · 4 steps

Range depends on sin 2θ, and complementary angles give the same sin 2θ.

1. Range formula. On level ground, a projectile thrown with speed u at angle θ lands at a horizontal distance that depends on θ only through sin 2θ.

   R = (u² sin 2θ)/g

2. Use the angle sum. Since α + β = 90°, we have β = 90° - α. Then sin 2β = sin(180° - 2α) = sin 2α.
3. Take the ratio. R₁/R₂ = (u² sin 2α / g)/(u² sin 2β / g) = (sin 2α)/(sin 2β) = 1. The speed u and g cancel because they are the same for both objects.
4. So. The two ranges are equal, and the ratio is 1 : 1, option (a).

The idea to keep. Same speed, complementary angles such as 30° and 60°: equal ranges every time. Heights and flight times differ, but the range does not.

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