Question 49: Motion in 2D & Vectors

Question

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 $$\sin 2 	heta$$ should be equal to one.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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 $\sin 2	heta$ 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 $R = (v^{2}/g) \cdot \sin(2	heta)$, where $v$ is the initial velocity of the projectile, $g$ is the acceleration due to gravity, and $	heta$ is the launch angle. For the range to be maximized, $\sin(2	heta)$ must be maximized, and the maximum value of $\sin(2	heta)$ is 1. This occurs when $2	heta = 90$ degrees, or $	heta = 45$ degrees, which corresponds to the assertion.

Answer

Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct and $$\mathbf{R}$$ is the correct explanation of $$\mathbf{A}$$

Answer

$$\mathbf{A}$$ is true but $$\mathbf{R}$$ is false

Answer

$$\mathbf{A}$$ is false but $$\mathbf{R}$$ is true

Answer

Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct but $$\mathbf{R}$$ is NOT the correct explanation of $$\mathbf{A}$$

Motion in 2D & Vectors

Choose the correct answer: