JEE MAIN - Physics (2023 - 6th April Morning Shift - No. 4)
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 $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct and $$\mathbf{R}$$ is the correct explanation of $$\mathbf{A}$$
$$\mathbf{A}$$ is true but $$\mathbf{R}$$ is false
$$\mathbf{A}$$ is false but $$\mathbf{R}$$ is true
Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct but $$\mathbf{R}$$ is NOT the correct explanation of $$\mathbf{A}$$
Explanation
Assertion A: When a body is projected at an angle of $45^{\circ}$, its range is maximum. This is true, and it's a well-established fact in physics. The maximum range of a projectile, assuming no air resistance and flat terrain, is achieved at an angle of $45^{\circ}$.
Reason R: For maximum range, the value of $\sin 2\theta$ should be equal to one. This is also true. The range of a projectile, again assuming no air resistance and flat terrain, can be calculated using the formula $R = (v^{2}/g) \cdot \sin(2\theta)$, where $v$ is the initial velocity of the projectile, $g$ is the acceleration due to gravity, and $\theta$ is the launch angle. For the range to be maximized, $\sin(2\theta)$ must be maximized, and the maximum value of $\sin(2\theta)$ is 1. This occurs when $2\theta = 90$ degrees, or $\theta = 45$ degrees, which corresponds to the assertion.
Reason R: For maximum range, the value of $\sin 2\theta$ should be equal to one. This is also true. The range of a projectile, again assuming no air resistance and flat terrain, can be calculated using the formula $R = (v^{2}/g) \cdot \sin(2\theta)$, where $v$ is the initial velocity of the projectile, $g$ is the acceleration due to gravity, and $\theta$ is the launch angle. For the range to be maximized, $\sin(2\theta)$ must be maximized, and the maximum value of $\sin(2\theta)$ is 1. This occurs when $2\theta = 90$ degrees, or $\theta = 45$ degrees, which corresponds to the assertion.
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