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 h 1 and h…

Question

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 $h_{1}$ and $h_{2}$ respectively, then $R = 4 \sqrt{h_{1} h_{2}}$

Reason R: Product of said heights. $h_{1} h_{2} = (\frac{u^{2} \sin^{2} θ}{2 g}) \cdot (\frac{u^{2} \cos^{2} θ}{2 g})$

Aicharya · Accepted Answer

Range of two balls are R 1 = u 2 sin 2 &#952; 1 g = R 2 = u 2 sin 2 &#952; 2 g . Now, maximum height by both balls are h 1 = u 2 sin 2 &#952; 1 2 g and h 2 = u 2 cos 2 &#952; 2 2 g &#8756; h 1 h 2 = u 2 sin 2 &#952; 2 g u 2 cos 2 &#952; 2 g = u 2 sin &#952; cos &#952; 2 g = R 4 &#8658; R = 4 h 1 h 2 Hence, both A and R are true and R is the correct explanation of A.

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.…

Solution