Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h₁ and h₂ respectively, then R = 4√h₁h₂
Reason R : Product of said heights.
h₁h₂ = ( (u²sin ²θ)/2g ) . ( (u²cos ²θ)/2g )
Choose the correct answer :

Solution

Physics sir · 3 steps

Same speed and same range means the angles are θ and 90° − θ, so one height has sin² and the other cos².

1. Complementary angles. Range R = (u² sin 2θ)/g is the same for θ and 90° - θ. So ball A goes at θ and ball B at 90° - θ.
2. The two heights. h₁ = (u² sin² θ)/2g. For B, sin(90° - θ) = cos θ, so h₂ = (u² cos² θ)/2g. Their product is exactly what Reason R states, so R is true.

   4√(h₁ h₂) = 4 × (u² sin θ cos θ)/2g = (u² (2 sin θ cos θ))/g = (u² sin 2θ)/g = R

3. So. Assertion A follows directly from the product in R, so both are true and R is the correct explanation. The answer is (a).

The idea to keep. Equal range at equal speed always means complementary angles. Then h₁ + h₂ = u²/2g and R = 4√(h₁ h₂) are both worth remembering.

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