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Question 3

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°, its range is maximum.
Reason R: For maximum range, the value of sin 2$$\theta$$ should be equal to one.
In the light of the above statements, choose the correct answer from the options given below:

The range of a projectile is given by $$R = \frac{u^2 \sin 2\theta}{g}$$. For maximum range, we need $$\sin 2\theta$$ to be maximum, i.e., $$\sin 2\theta = 1$$, which gives $$2\theta = 90°$$ or $$\theta = 45°$$. Thus Assertion A is true: at $$\theta = 45°$$, the range is indeed maximum.

Reason R states that for maximum range, $$\sin 2\theta$$ should equal one, which is exactly the condition derived above. This is also true, and it directly explains why $$\theta = 45°$$ gives maximum range.

Since both A and R are correct and R is the correct explanation of A, the answer is Option C.

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