A projectile is fired from level ground at an | vedclass

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

Question

(C) Let $H$ be the maximum height and $R$ be the horizontal range of the projectile.From the geometry of the trajectory,the highest point is at a hori

Vedclass · Accepted Answer

$	an \phi = \frac{1}{2} 	an 	heta$

Vedclass · Answer

(C) Let $H$ be the maximum height and $R$ be the horizontal range of the projectile.From the geometry of the trajectory,the highest point is at a horizontal distance of $R/2$ from the launch point.The elevation angle $\phi$ is defined as the angle whose tangent is the ratio of the maximum height to the horizontal distance of the highest point from the launch point.Therefore,$	an \phi = \frac{H}{R/2}$.Substituting the standard formulas $H = \frac{u^2 \sin^2 	heta}{2g}$ and $R = \frac{u^2 \sin 2	heta}{g}$,we get:$	an \phi = \frac{u^2 \sin^2 	heta / 2g}{(u^2 \sin 2	heta / g) / 2} = \frac{u^2 \sin^2 	heta / 2g}{u^2 \sin 2	heta / 2g} = \frac{\sin^2 	heta}{\sin 2	heta}$.Using the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$,we have:$	an \phi = \frac{\sin^2 	heta}{2 \sin 	heta \cos 	heta} = \frac{1}{2} \frac{\sin 	heta}{\cos 	heta} = \frac{1}{2} 	an 	heta$.

$A$ projectile is fired from level ground at an angle $\theta$ above the horizontal. The elevation angle $\phi$ of the highest point as seen from the launch point is related to $\theta$ by the relation

Similar Questions

Galileo writes that for angles of projection of a projectile at angles $(45^\circ + \theta)$ and $(45^\circ - \theta)$,the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45^\circ$):

$A$ projectile is thrown at an angle of $\pi/3$ with the horizontal,reaching a maximum height $Y$. If another projectile is thrown with the same initial velocity at an angle of $\pi/6$,what will be the maximum height attained?

At what angle of elevation should a projectile be projected with a velocity of $20 \, m/s$ to reach a maximum height of $10 \, m$ (in $^{\circ}$)?

$A$ projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle $\alpha$ with the horizontal is

$A$ ball having kinetic energy $KE$ is projected at an angle of $60^{\circ}$ from the horizontal. What will be the kinetic energy of the ball at the highest point of its flight?

Vedclass Test Series

Exam Paper Generator

Online Exam Module