A projectile thrown at an angle of $30^{o}$ with the horizontal has a range $R_{1}$ and attains a maximum height $h_{1}$ . Another projectile thrown, with the same speed, at an angle $30^{o}$ with the vertical, has a range $R_{2}$ and attains a maximum height $h_{2}$ . The relation between $R_{1}$ and $R_{2}$ is :-

Open in App

Solution

For first projectile motion, the angle from horizontal is given as,

$θ_{1} = 30^{\circ}$

For second projectile motion, the angle from horizontal is given as,

$θ_{2} = 90^{\circ} - 30^{\circ}$

$= 60^{\circ}$

The range $R_{1}$ is given as,

$R_{1} = \frac{u^{2} sin 2 θ}{g}$

$= \frac{u^{2} sin (2 \times 30^{\circ})}{g}$

$= \frac{\sqrt{3} u^{2}}{2 g}$

The range $R_{2}$ is given as,

$R_{2} = \frac{u^{2} sin 2 θ}{g}$

$= \frac{u^{2} sin (2 \times 60^{\circ})}{g}$

$= \frac{\sqrt{3} u^{2}}{2 g}$

Thus, the relation between $R_{1}$ and $R_{2}$ is $R_{1} = R_{2}$ .

Suggest Corrections

Similar questions

A projectile thrown at an angle of $30^{\circ}$ with the horizontal has a range $R_{1}$ . Another projectile thrown, with the same velocity, at an angle $30^{\circ}$ with the vertical, has a range $R_{2}$ . The relation between $R_{1}$ and $R_{2}$ is

A projectile thrown with an initial velocity $u$ has the same range R when the maximum height attained by it is either $h_{1}$ or $h_{2} .$ Then $R, h_{1}$ and $h_{2}$ are related as