(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 2 Motion in a 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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2 Motion in a Plane

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Mix Examples-Motion in Plane

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$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

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The range of a projectile of mass $1\, kg$ is $80\, m$ while it attains a maximum height of $20\, m$. Its change in momentum during the complete motion is ............ $N-s$.

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The figure shows the $(x, t)$ and $(y, t)$ diagrams of a particle moving in $2$ dimensions. If the particle has a mass of $500 \, g$,find the force (magnitude and direction) acting on the particle.

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Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along a circular path of radius $0.5\,m$ at constant speeds $0.5\,m/s$ and $1.5\,m/s$,respectively. The time when they collide with each other is ........ $\text{s}$.

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Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?

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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

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

The range of a projectile of mass $1\, kg$ is $80\, m$ while it attains a maximum height of $20\, m$. Its change in momentum during the complete motion is ............ $N-s$.

The figure shows the $(x, t)$ and $(y, t)$ diagrams of a particle moving in $2$ dimensions. If the particle has a mass of $500 \, g$,find the force (magnitude and direction) acting on the particle.

Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along a circular path of radius $0.5\,m$ at constant speeds $0.5\,m/s$ and $1.5\,m/s$,respectively. The time when they collide with each other is ........ $\text{s}$.

Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?

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