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 :-

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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 $R_{1} = R_{2}$ .

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A projectile thrown at an angle of 30o with the horizontal has a range R1 and attains a maximum height h1 . Another projectile thrown, with the same speed, at an angle 30o with the vertical, has a range R2 and attains a maximum height h2 . The relation between R1 and R2 is :-