Question

If $R$ is the maximum horizontal range of a particle, then the greatest height attained by it is:

• A. $R$
• B. $2R$
• C. $\frac{R}{2}$
• D. $\frac{R}{4}$

Answer 1

The correct option is D $\frac{R}{4}$

Let R is the maximum horizontal range of the projectile. The formula of the range is given by :

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

For maximum range,

$sin2\theta =1$

$\theta ={45}^0$

Putting the value of $\theta$ in the above equation, we get :

$R=\frac{u^2}{g}$

The formula for the maximum height attained is given by :

$H=\frac{u^{2}si{n}^2\theta }{2g}$

$H=\frac{1}{2}\times \frac{u^2}{g}\times si{n}^2\left(45\right)$

$H=\frac{1}{2}\times R\times si{n}^2\left(45\right)$

$H=\frac{R}{4}$

So, the greatest height attained by the particle is $\frac{R}{4}$. Hence, this is the required solution.