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

$R=\sqrt{4ℎ1ℎ2}.$

Reason R: Product of said heights.

$h_1h_2=(\frac{u^2sin^2θ}{2g}).(\frac{u^2cos^2θ}{2g})$

• 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 1

Answer: (A)

Both A and R are true and R is the correct explanation of A.

Answer 2

The correct Option is(A): Both A and R are true and R is the correct explanation of A.

$h_1=\frac{u^2sin^2θ}{2g}$

$h_2=\frac{u^2cos^2θ}{2g}$

∴ $\sqrt{h_1h_2}=\frac{u^2sinθcosθ}{2g}$

$=\frac{R}{4}$

$⇒R=4\sqrt{h_1h_2}$