Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : When a body is projected at an angle 45°, it's range is maximum.
Reason R : For maximum range, the value of sin 2 θ should be equal to one.
In the light of the above statements, choose the correct answer from the options given below:

Solution

Physics sir · 3 steps

Range depends on sin 2θ, and a sine can be at most 1. That happens at 2θ = 90°.

1. R = (u² sin 2θ)/g

2. Check Reason R. For a fixed launch speed u, the only part of R that changes with angle is sin 2θ. A sine is never more than 1, so the range is largest when sin 2θ = 1. R is true.
3. Check Assertion A. sin 2θ = 1 means 2θ = 90°, so θ = 45°. On level ground, a projectile thrown at 45° has the maximum range, Rₘₐₓ = u²/g. A is true.
4. So. Both are true, and A follows directly from R: the 45° angle is exactly the angle that makes sin 2θ = 1. The answer is (a).

The idea to keep. In assertion-reason questions, check whether the reason is the step you would actually use to prove the assertion. If A falls straight out of R, R is the correct explanation.

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