Two bodies are thrown up at angles of 45^o and 60^o , respectively, with the horizontal. If bo

English

Gujarati

Hindi

3-2.Motion in Plane

medium

Two bodies are thrown up at angles of $45^o$ and $60^o$, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

$\sqrt{\frac{2}{3}}$

$\frac{2}{\sqrt 3}$

$\sqrt{\frac{3}{2}}$

$\frac{\sqrt 3}{2}$

Solution

$\mathrm{H}_{\max }=\frac{\mathrm{u}^{2} \sin ^{2} \theta}{2 \mathrm{g}}$

According to problem

$\frac{\mathrm{u}_{1}^{2} \sin ^{2} 45^{\circ}}{2 \mathrm{g}}=\frac{\mathrm{u}_{2}^{2} \sin ^{2} 60^{\circ}}{2 \mathrm{g}}$

$\Rightarrow \frac{\mathrm{u}_{1}^{2}}{\mathrm{u}_{2}^{2}}=\frac{\sin ^{2} 60^{\circ}}{\sin ^{2} 45^{\circ}} \Rightarrow \frac{\mathrm{u}_{1}}{\mathrm{u}_{2}}=\frac{\sqrt{3} / 2}{1 / \sqrt{2}}=\sqrt{\frac{3}{2}}$

Standard 11

Physics

A stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height $h$ and then attain a maximum height $2 h$ above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending, then the ratio of the speed of the bird to the horizontal speed of the stone is

normal

A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3\, ms^{-2}$ for $ 0.5\, minutes$. If the maximum height reached by it is $80\, m$, then the angle of projection is (Take $g = 10\, ms^{-2}$)

hard

A projectile is thrown with velocity $v$ at an angle $\theta$ with horizontal. When the projectile is at a height equal to half of the maximum height, the vertical component of the velocity of projectile is ………..

medium

A particle of mass $m$ is projected with velocity $v$ making an angle of $45^o $ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

medium

(AIPMT-2008)

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)

Two bodies are thrown up at angles of $45^o$ and $60^o$, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

Solution

Similar Questions

A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3\, ms^{-2}$ for $ 0.5\, minutes$. If the maximum height reached by it is $80\, m$, then the angle of projection is (Take $g = 10\, ms^{-2}$)

A projectile is thrown with velocity $v$ at an angle $\theta$ with horizontal. When the projectile is at a height equal to half of the maximum height, the vertical component of the velocity of projectile is ………..

A particle of mass $m$ is projected with velocity $v$ making an angle of $45^o $ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

Start a Free Trial Now