Question

Assertion :When a body is projected at an angle ${45}^0$, its maximum height is half of horizontal range. Reason: Horizontal range $=\frac{U^{2}sin2\theta }{g}$ and maximum height $=\frac{U^{2}si{n}^2\theta }{2g}$.

• A. Both Assertion and Reason are true and Reason is correct explanation of the Assertion.
• B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
• C. Assertion is true, but the Reason is false.
• D. Assertion is false, but the Reason is true.

Answer 1

The correct option is D Assertion is false, but the Reason is true.

Horizontal range, $R=\frac{U^{2}sin2\theta }{g}$

at $\theta ={45}^{\circ }$, $R=\frac{U^2}{g}$

Maximum height $H=\frac{U^{2}si{n}^2\theta }{2g}$

at $\theta ={45}^{\circ }$, $H=\frac{U^2}{4g}$

We can see that maximum height is not half of horizontal range for projection angle= $\theta ={45}^{\circ }$.

So, reason is true but the assertion is false.