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:
Solution
<b>Assertion A</b>: 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 $45^{\circ}$.
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<b>Reason R</b>: 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.
About this question
Subject: Physics · Chapter: Kinematics · Topic: Motion in a Straight Line
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