A particle is projected with a velocity v suc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: Horizontal range $(R)$ $= 2 	imes$ Maximum height $(H)$.Formula for range: $R = \frac{v^{2} \sin 2	heta}{g}$.Formula for maximum height:

Vedclass · Accepted Answer

$ \frac{4 v^{2}}{5 g} $

Vedclass · Answer

(C) Given: Horizontal range $(R)$ $= 2 	imes$ Maximum height $(H)$.Formula for range: $R = \frac{v^{2} \sin 2	heta}{g}$.Formula for maximum height: $H = \frac{v^{2} \sin^{2} 	heta}{2g}$.According to the problem: $\frac{v^{2} \sin 2	heta}{g} = 2 	imes \frac{v^{2} \sin^{2} 	heta}{2g}$.Simplifying: $\sin 2	heta = \sin^{2} 	heta$.Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$: $2 \sin 	heta \cos 	heta = \sin^{2} 	heta$.Dividing by $\sin 	heta$ (assuming $	heta 
eq 0$): $2 \cos 	heta = \sin 	heta$,which means $	an 	heta = 2$.From $	an 	heta = 2$,we have $\sin 	heta = \frac{2}{\sqrt{5}}$ and $\cos 	heta = \frac{1}{\sqrt{5}}$.Substituting these into the range formula: $R = \frac{v^{2} (2 \sin 	heta \cos 	heta)}{g} = \frac{2v^{2}}{g} 	imes \frac{2}{\sqrt{5}} 	imes \frac{1}{\sqrt{5}} = \frac{4v^{2}}{5g}$.

$A$ particle is projected with a velocity $v$ such that its horizontal range is twice the greatest height attained. The horizontal range is

Similar Questions

What is the angle between the velocity and acceleration of a projectile at its maximum height (in $°$)?

The range of a projectile for a given initial velocity is maximum when the angle of projection is $45^\circ$. The range will be minimum,if the angle of projection is ......... $^\circ$.

$A$ ball is thrown at $30^{\circ}$ with the horizontal from the top of a roof $20 \,m$ high with a speed of $13 \,ms^{-1}$. At what distance from the throwing point will the ball, once again, be at a height of $20 \,m$ from the ground (in $\,m$)? $(g = 10 \,ms^{-2})$

If the time of flight of a bullet over a horizontal range $R$ is $T \ s$,the inclination of the direction of projection to the horizontal is

If a body $A$ of mass $M$ is thrown with velocity $v$ at an angle of $30^{\circ}$ to the horizontal and another body $B$ of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal,the ratio of the horizontal range of $A$ to $B$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module