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  4. Assertion The range of a projectile is maximum at 45°. Reason At θ=45°, the value of sin θ is maximum.

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Q. Assertion The range of a projectile is maximum at $45^{\circ}$.
Reason At $\theta=45^{\circ}$, the value of $\sin \theta$ is maximum.

Motion in a Plane

Solution:

Horizontal range, $R=\frac{u^{2} \sin 2 \theta}{g}$
At, $ \theta=45^{\circ}, \sin 2 \theta=1 $
$ \therefore R_{\max }=\frac{u^{2}}{g}=$ maximum range
$ \because \sin \theta=1 $ (maximum), at $ \theta=90^{\circ}$
Therefore, Assertion is correct but Reason is incorrect.