Question

Assertion The maximum height of projectile is always 25% of the maximum range.
Reason For maximum range, projectile should be projected at 90°.

Moderate

A

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B

Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion.
C

Assertion is correct but Reason is incorrect.
D

Assertion is incorrect but Reason is correct.

Solution

To obtain maximum range, angle of projection must be 45°, i.e., $θ$ = 45°.
$R_{\max} = \frac{u^{2} \sin (2 \times 45 °)}{g} = \frac{u^{2}}{g}$
$∵ H_{\max} = \frac{u^{2} \sin^{2} 45 °}{2 g} = \frac{u^{2}}{4 g} = \frac{R_{\max}}{4}$
So, H_max is 25 % of R_max

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