A particle is projected from ground with an initial speed upsilon at an angle θ with horizont

English

Gujarati

Hindi

3-2.Motion in Plane

hard

A particle is projected from the ground with an initial speed $\upsilon $ at an angle $\theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

A

$\frac{\upsilon }{2}\sqrt {1 + 2\,\,{{\cos }^{2\,}}\theta } $

B

$\frac{\upsilon }{2}\sqrt {1 + {{\cos }^{2\,}}\theta } $

C

$\frac{\upsilon }{2}\sqrt {1 + 3\,\,{{\cos }^{2\,}}\theta } $

D

$\upsilon \,\cos \,\theta $

Solution

Average velocity $=\frac{\text { Displacement }}{\text { Time }}$

$v_{w_{w}}=\frac{\sqrt{H^{2}+\frac{R^{2}}{4}}}{T / 2}$

Here, $\quad \mathrm{H}=$ maximum height $=\frac{v^{2} \sin ^{2} \theta}{2 g}$

$\mathrm{R}=\mathrm{range}=\frac{\mathrm{v}^{2} \sin 2 \theta}{\mathrm{g}}$

and $\quad \mathrm{T}=$ time of flight $=\frac{2v \sin \theta}{\mathrm{g}}$

$\therefore \quad \mathrm{U}_{\mathrm{av} .}=\frac{\mathrm{v}}{2} \sqrt{1+3 \cos ^{2} \theta}$

Standard 11

Physics

Share

Similar Questions

A projectile is thrown with a velocity of $50\,\, ms^{^{-1}}$ at an angle of $53^o$ with the horizontal The equation of the trajectory is given by

medium

A projectile is thrown with a velocity of $10\,m / s$ at an angle of $60^{\circ}$ with horizontal. The interval between the moments when speed is $\sqrt{5 g}\,m / s$ is $……….\,s$ $\left(g=10\,m / s ^2\right)$.

hard

Three balls of same masses are projected with equal speeds at angle $15^{\circ}, 45^{\circ}, 75^{\circ}$, and their ranges are respectively $R_1, R_2$ and $R_3$, then

medium

A projectile is fired from the surface of the earth with a velocity of $5 \,m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \,m s^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $\,m s^{-1}$) is
(Given $g = 9.8 \,m s^{-2}$)

medium

(AIPMT-2014)

Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : When a body is projected at an angle $45^{\circ}$, it's range is maximum.

Reason $R$ : For maximum range, the value of $\sin 2 \theta$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below :

medium

(JEE MAIN-2023)