Question

Consider the following statements $A$ and $B$ and mark the correct option.
$A)$ The maximum range is $4$ times the maximum height attained during its flight in the case of a projectile.
$B)$ In the case of a projectile the range $R$ is related to the time of flight $T$ as $R=5T^2$. If $g=10m{s}^{-2}$ the angle of projection is ${45}^o$.

• A. Both $A$ and $B$ are true
• B. $A$ is true but $B$ is false
• C. $B$ is true but $A$ is false
• D. Both $A$ and $B$ are false

Answer 1

Answer: (A)

Both $A$ and $B$ are true

Projectile's maximum height and range are given by

$H=\frac{V_o^2{\sin }^2\theta }{2g}\&R=\frac{V_o^2\sin 2\theta }{g}$

$\frac{H}{R}=\frac{\tan \theta }{4}=\frac{1}{4}$

Range is maximum when $\theta ={45}^{\circ }$

$\Rightarrow R=4H$

Projectile flight of time and range are given by

$T=\frac{2V_o\sin \theta }{g}\&R=\frac{V_o^2\sin 2\theta }{g}$

$R=\frac{V_o^2}{g}(taking\theta ={45}^0)T^2=\frac{V_o^2}{5g}(taking\theta ={45}^0)\Rightarrow \frac{R}{T^2}=5$