Given below are two statements: one is labelled as Assertion A and...

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:

Options

A $A$ is false but $R$ is true
B $A$ is true but $R$ is false
C
Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$
D
Both $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$

Correct answer

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

Step-by-step solution

Horizontal range of a projectile from a horizontal plane is given by, $R = \dfrac{{u}^{2}\sin 2\theta}{g}$ .
Clearly for maximum range, $\sin 2\theta = 1$ .
Therefore, $\theta = 45 °$ .

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