Speed of a projectile at its maximum height is frac {√ 3}{2} times its initial speed. If range of

English

Gujarati

Hindi

3-2.Motion in Plane

medium

The speed of a projectile at its maximum height is $\frac {\sqrt 3}{2}$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it, $P$ is equal to

A

$\frac {4}{3}$

B

$2 \sqrt 3$

C

$4 \sqrt 3$

D

$\frac {3}{4}$

Solution

Given: $\frac{\sqrt{3} u}{2}=u \cos \theta=$ speed at maximum height

${\cos \theta=\frac{\sqrt{3}}{2}}$

Or ${\theta=30^{\circ}}$

Given that; $p H_{\max }=R$

We know, $H_{\max }=\frac{R \tan \theta}{4}$

$\therefore \quad P=\frac{4}{\tan \theta}=\frac{4}{\tan 30^{\circ}}=4 \sqrt{3}$

Standard 11

Physics

Share

Similar Questions

A projectile $A$ is thrown at an angle $30^{\circ}$ to the horizontal from point $P$. At the same time another projectile $B$ is thrown with velocity $v_2$ upwards from the point $Q$ vertically below the highest point $A$ would reach. For $B$ to collide with $A$, the ratio $\frac{v_2}{v_1}$ should be

medium

A player kicks a football with an initial speed of $25\, {ms}^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g $=10 \,{ms}^{-2}$ )

medium

(JEE MAIN-2021)

Which of the following is the graph between the height $(h)$ of a projectile and time $(t)$, when it is projected from the ground

easy

The maximum height attained by a projectile is increased by $10\,\%$ by increasing its speed of projection, without changing the angle of projection. The percentage increases in the horizontal range will be $………..\,\%$

easy

A stone is projected with a velocity $20 \sqrt{2}\,m / s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is $……….\,m/s$ (take $g=10\,m / s ^2$ )

hard