(B) Let the two boys meet at point $C$ after time $t$ from the start.In time $t$,the boy from $B$ covers distance $BC = v_1 t$.The boy from $A$ covers

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(B) Let the two boys meet at point $C$ after time $t$ from the start.In time $t$,the boy from $B$ covers distance $BC = v_1 t$.The boy from $A$ covers distance $AC = v t$.Since the boy at $B$ runs perpendicular to $AB$,$\triangle ABC$ is a right-angled triangle with $\angle B = 90^{\circ}$.Using the Pythagorean theorem: $(AC)^2 = (AB)^2 + (BC)^2$.Substituting the values: $(vt)^2 = a^2 + (v_1 t)^2$.$v^2 t^2 - v_1^2 t^2 = a^2$.$t^2 (v^2 - v_1^2) = a^2$.$t = \sqrt{\frac{a^2}{v^2 - v_1^2}}$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

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Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$,where $t$ is

AIPMT 2005 All AIPMT

A
$a/\sqrt{v^2 + v_1^2}$
B
$\sqrt{a^2 / (v^2 - v_1^2)}$
C
$a / (v - v_1)$
D
$a / (v + v_1)$

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3-2.Motion in Plane

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Mix Examples-Motion in Plane

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AIPMT 2005 Paper All AIPMT years →

At a given instant of time,the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

DifficultAP EAMCET 2005

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The velocities of two particles $A$ and $B$,separated by a distance of $20 \ m$,are as shown in the figure. Find the angular velocity of $B$ with respect to $A$ in $rad/s$.

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$A$ boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored,the forces acting on the ball at the position $X$ are represented by

EasyKCET 2010

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$A$ projectile fired at $30^{\circ}$ to the ground is observed to be at the same height at time $t_1 = 3 \, s$ and $t_2 = 5 \, s$ after projection,during its flight. The speed of projection of the projectile is $......... \, m \, s^{-1}$ (Given $g = 10 \, m \, s^{-2}$).

DifficultJEE MAIN 2023

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$A$ point moves in the $xy$-plane according to the following equations: $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

MediumTS EAMCET 2020

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Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$,where $t$ is

Similar Questions

At a given instant of time,the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

The velocities of two particles $A$ and $B$,separated by a distance of $20 \ m$,are as shown in the figure. Find the angular velocity of $B$ with respect to $A$ in $rad/s$.

$A$ boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored,the forces acting on the ball at the position $X$ are represented by

$A$ projectile fired at $30^{\circ}$ to the ground is observed to be at the same height at time $t_1 = 3 \, s$ and $t_2 = 5 \, s$ after projection,during its flight. The speed of projection of the projectile is $......... \, m \, s^{-1}$ (Given $g = 10 \, m \, s^{-2}$).

$A$ point moves in the $xy$-plane according to the following equations: $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

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