Question

A projectile when projected either with an angle $\theta or2\theta$ with the horizontal has the same range R.Then the value of $\theta$ is .

• A. ${30}^0$
• B. ${45}^0$
• C. ${15}^0$
• D. ${90}^0$

Answer 1

Answer: (A)

${30}^0$

Lets consider, $u=$ Initial velocity of projectile

A projectile when projected wither with an angle $\theta$ or $2\theta$ with the Horizontal and has the same range.

The horizontal range in projectile motion,

$R=\frac{u^{2}sin2\theta }{g}$ (projected with angle $\theta$)

$R=\frac{u^{2}sin4\theta }{g}$ (projected with angle $2\theta$)

According to question,

$\frac{u^{2}sin2\theta }{g}=\frac{u^{2}sin4\theta }{g}$

$sin2\theta =2sin2\theta .cos2\theta$

$cos2\theta =\frac{1}{2}$

$2\theta =co{s}^{-1}\left(0.5\right)$

$2\theta ={60}^0$

$\theta ={30}^0$

The correct option is A.