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^\circ , it's 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:

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

Both A and R are correct but R is NOT the correct explanation of A

Motion in A Plane PYQ — JEE Main 2023 · 6 Apr · Shift 1 · Q46 with Solution

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Correct answer: A

For a projectile projected with speed $u$ at an angle $\theta$ with the horizontal, the horizontal range is

$R = \frac{u^2 \sin 2\theta}{g}$

where $g$ is acceleration due to gravity.

Assertion A says: When a body is projected at an angle $45^\circ$ , its range is maximum.

From the formula,

$R \propto \sin 2\theta$

The maximum value of $\sin 2\theta$ is $1$ .

So maximum range occurs when

$\sin 2\theta = 1$

which gives

$2\theta = 90^\circ \Rightarrow \theta = 45^\circ$

Hence, Assertion A is true.

Reason R says: For maximum range, the value of $\sin 2\theta$ should be equal to one.

This is directly true, because from

$R = \frac{u^2 \sin 2\theta}{g}$

range is maximum when $\sin 2\theta$ is maximum, and its maximum value is $1$ .

Hence, Reason R is true.

Reason R correctly explains why the range is maximum at $45^\circ$ :

$\sin 2\theta = 1 \Rightarrow 2\theta = 90^\circ \Rightarrow \theta = 45^\circ$

So R is the correct explanation of A.

Both Assertion A and Reason R are correct, and Reason R correctly explains Assertion A.

Therefore, the correct option is:

$\boxed{\text{A}}$