(A) Let the horizontal direction be the $x$-axis and the vertical direction be the $y$-axis.At time $t$,the velocity vector of the first particle is $

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

(A) Let the horizontal direction be the $x$-axis and the vertical direction be the $y$-axis.At time $t$,the velocity vector of the first particle is $\vec{v}_1 = u_1 \hat{i} - gt \hat{j}$.The velocity vector of the second particle is $\vec{v}_2 = -u_2 \hat{i} - gt \hat{j}$.Since the velocities are mutually perpendicular,their dot product must be zero: $\vec{v}_1 \cdot \vec{v}_2 = 0$.$(u_1 \hat{i} - gt \hat{j}) \cdot (-u_2 \hat{i} - gt \hat{j}) = 0$.$-u_1 u_2 + g^2 t^2 = 0$.$g^2 t^2 = u_1 u_2$.$t = \frac{\sqrt{u_1 u_2}}{g}$.

Class 11 Physics 3-2.Motion in Plane Horizontal Projectile Motion

Difficult

Two particles are simultaneously projected in opposite directions horizontally from a given point in space,where gravity $g$ is uniform. If $u_1$ and $u_2$ are their initial speeds,then the time $t$ after which their velocities are mutually perpendicular is given by

A
$\frac{\sqrt{u_1 u_2}}{g}$
B
$\frac{\sqrt{u_1^2+u_2^2}}{g}$
C
$\frac{\sqrt{u_1(u_1+u_2)}}{g}$
D
$\frac{\sqrt{u_2(u_1+u_2)}}{g}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

3-2.Motion in Plane

Subtopic

Horizontal Projectile Motion

The horizontal range and maximum height attained by a projectile are $R$ and $H$,respectively. If a constant horizontal acceleration $a=g/4$ is imparted to the projectile due to wind,then its horizontal range and maximum height will be

Medium

View Solution

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$,where $\alpha$ and $\beta$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by:

DifficultJEE MAIN 2021

View Solution

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

View Solution

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings $100 \; m$ apart and of the same height of $200 \; m$ with the same velocity of $25 \; m/s$. When and where will the two bullets collide? $(g = 10 \; m/s^2)$

MediumNEET 2019

View Solution

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways, then the product $t_1 t_2$ is proportional to

EasyAP EAMCET 2012

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Two particles are simultaneously projected in opposite directions horizontally from a given point in space,where gravity $g$ is uniform. If $u_1$ and $u_2$ are their initial speeds,then the time $t$ after which their velocities are mutually perpendicular is given by

Similar Questions

The horizontal range and maximum height attained by a projectile are $R$ and $H$,respectively. If a constant horizontal acceleration $a=g/4$ is imparted to the projectile due to wind,then its horizontal range and maximum height will be

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings $100 \; m$ apart and of the same height of $200 \; m$ with the same velocity of $25 \; m/s$. When and where will the two bullets collide? $(g = 10 \; m/s^2)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module