Two projectiles are projected with the same i | vedclass

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

Question

(B) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$, where $u$ is the initial velocity and $	heta$

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(B) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$, where $u$ is the initial velocity and $	heta$ is the angle of projection.Since both projectiles have the same initial velocity $u$, the range is directly proportional to $\sin(2	heta)$, i.e.,$R \propto \sin(2	heta)$.For the first projectile, $	heta_1 = 15^{\circ}$, so $R_1 \propto \sin(2 	imes 15^{\circ}) = \sin(30^{\circ}) = 1/2$.For the second projectile, $	heta_2 = 30^{\circ}$, so $R_2 \propto \sin(2 	imes 30^{\circ}) = \sin(60^{\circ}) = \sqrt{3}/2$.The ratio of their ranges is $\frac{R_1}{R_2} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}}$.Given the ratio is $1:x$, we have $1:x = 1:\sqrt{3}$.Therefore, $x = \sqrt{3}$.

Two projectiles are projected with the same initial velocities at $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

Similar Questions

$A$ body is projected at an angle of $30^{\circ}$ with the horizontal with momentum $p$. At its highest point,the magnitude of the momentum is

$A$ projectile is thrown at a speed which is twice its speed at its maximum height. If $R$ and $H$ are its range and maximum height respectively, then the ratio $\frac{R}{H}$ is

$A$ player can throw a ball to a maximum horizontal distance of $80 \,m$. If he throws the ball vertically with the same velocity, then the maximum height reached by the ball is (in $\,m$)

$A$ grasshopper can jump a maximum distance of $1.6 \; m$. It spends a negligible amount of time on the ground. How far can it go in $10 \; s$?

In a projectile motion,the velocity at maximum height is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module