Question

The speed of a projectile at the maximum height is half of its initial speed . Find the ratio of range of projectile to the maximum height attained ?

Answer 1

Answer:

4/√3

Explanation:

Refer to the material.

Answer 2

At maximum height, only horizontal velocity exists. Thus,

$\displaystyle\longrightarrow\sf{u\cos\theta=\dfrac{u}{2}}$

$\displaystyle\longrightarrow\sf{\cos\theta=\dfrac{1}{2}}$

$\displaystyle\longrightarrow\sf{\theta=60^o}$

Then,

$\displaystyle\longrightarrow\sf{\dfrac{R}{H}=\dfrac{\left(\dfrac{u^2\cdot2\sin\theta\cos\theta}{g}\right)}{\left(\dfrac{u^2\sin^2\theta}{2g}\right)}}$

$\displaystyle\longrightarrow\sf{\dfrac{R}{H}=\dfrac{4\cos\theta}{\sin\theta}$

$\displaystyle\longrightarrow\sf{\dfrac{R}{H}=4\cot60^o}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\dfrac{R}{H}=\dfrac{4}{\sqrt3}}}}$