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√(h₁ h₂) Reason R: Product of said heights. h₁ h₂ = ((u² sin ²θ)/(2g)) · ((u² cos ²θ)/(2g)) Choose the correct answer: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is NOT the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a). Same range means angles θ and 90° - θ, so h₁ = (u²sin ²θ)/(2g), h₂ = (u²cos ²θ)/(2g): R is true. h₁ h₂ = (u⁴sin ²θcos ²θ)/(4g²) and R² = (4u⁴sin ²θcos ²θ)/(g²) = 16h₁ h₂ So R = 4√(h₁ h₂): A is true and follows directly from R. So the answer is (a).

Given below are two statements. One is labelled as Assertion A and… | JEE Main 2022 (25 Jun, Shift 2)

Q17JEE Main 2022 · 25 JUN · SHIFT 2Medium

Comparing Two Projectiles

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 $R = 4\sqrt{h_1 h_2}$

Reason R: Product of said heights.

$h_1 h_2 = \left(\frac{u^2 \sin^2\theta}{2g}\right) \cdot \left(\frac{u^2 \cos^2\theta}{2g}\right)$

Choose the correct answer:

Show answer and solution

Answer: (a)

Same range means angles $\theta$ and $90^\circ - \theta$ , so $h_1 = \frac{u^2\sin^2\theta}{2g}$ , $h_2 = \frac{u^2\cos^2\theta}{2g}$ : R is true.
$h_1 h_2 = \frac{u^4\sin^2\theta\cos^2\theta}{4g^2}$ and $R^2 = \frac{4u^4\sin^2\theta\cos^2\theta}{g^2} = 16h_1 h_2$
So $R = 4\sqrt{h_1 h_2}$ : A is true and follows directly from R.
So the answer is (a).

Report a mistake

Comparing Two Projectiles question from JEE Main 2022 (25 Jun, Shift 2)

More questions on Comparing Two Projectiles