Question

At what angle with the horizontal should a ball be thrown so that the range $R$ is related to the time of flight $\left(T\right)$ as $R=5T^2?(\text{Take g}=10{\text{m/s}}^2)$

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Given, $\frac{R}{T^2}=5$
We know that
$R=\frac{u^2\text{sin}2\theta }{g};T=\frac{2\text{u sin}\theta }{g}$
$\therefore \frac{R}{T^2}=g\frac{\text{sin}2\theta }{4{\text{sin}}^2\theta }=\frac{\text{g cot}\theta }{2}=5\text{cot}\theta [Since,sin2\theta =2\sin \theta \cos \theta ]$
Hence, $5=5\text{cot}\theta$
$\Rightarrow \theta ={45}^{\circ }$