Three projectiles A, B and C are projected at | vedclass

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

Question

(D) The horizontal range $R$ of a projectile is given by the formula: $R = \frac{v_{0}^{2} \sin(2	heta)}{g}$,where $v_{0}$ is the initial velocity,$\

Vedclass · Accepted Answer

$R_{A}=R_{C} < R_{B}$

Vedclass · Answer

(D) The horizontal range $R$ of a projectile is given by the formula: $R = \frac{v_{0}^{2} \sin(2	heta)}{g}$,where $v_{0}$ is the initial velocity,$	heta$ is the angle of projection,and $g$ is the acceleration due to gravity.Since $v_{0}$ and $g$ are constant for all three projectiles,$R \propto \sin(2	heta)$.For projectile $A$: $	heta_{A} = 30^{\circ}$,so $R_{A} \propto \sin(2 	imes 30^{\circ}) = \sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.For projectile $B$: $	heta_{B} = 45^{\circ}$,so $R_{B} \propto \sin(2 	imes 45^{\circ}) = \sin(90^{\circ}) = 1$.For projectile $C$: $	heta_{C} = 60^{\circ}$,so $R_{C} \propto \sin(2 	imes 60^{\circ}) = \sin(120^{\circ}) = \sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.Comparing the values: $R_{A} = \frac{\sqrt{3}}{2}$,$R_{B} = 1$,and $R_{C} = \frac{\sqrt{3}}{2}$.Therefore,$R_{A} = R_{C} < R_{B}$.

Three projectiles $A, B$ and $C$ are projected at an angle of $30^{\circ}, 45^{\circ}, 60^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are the ranges of $A, B$ and $C$ respectively,then (velocity of projection is the same for $A, B$ and $C$):

Similar Questions

One second after projection, a projectile is travelling in a direction inclined at $45^{\circ}$ to the horizontal. After two more seconds, it is travelling horizontally. Then the magnitude of the initial velocity of the projectile is $(g = 10 \,ms^{-2})$

In the given figure for a projectile,find the relation for $y$ in terms of $x_1, x_2$ and $\theta$.

The equation of a projectile is $y = 16x - \frac{5x^2}{4}$. The horizontal range is .......... $m$.

$A$ missile is fired for maximum range with an initial velocity of $20\; m/s$. If $g = 10\; m/s^2$,the range of the missile is ...... $m$.

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module