(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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Two particles $A$ and $B$ are moving in the $XY$ plane. Particle $A$ moves along a line with equation $y = x$,while particle $B$ moves along the $X$-axis such that their $X$-coordinates are always equal. If particle $B$ moves with a uniform speed of $3 \ m/s$,what is the speed of particle $A$?

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$A$ block of mass $5\,kg$ is moving horizontally at a speed of $1.5\,m/s$. $A$ perpendicular force of $5\,N$ acts on it for $4\,s$. What will be the distance of the block from the point where the force started acting?

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$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is:

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$A$ point traversed $3/4$th of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is

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Two stones are projected so as to reach the same horizontal range on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then,the angle of projection of the stone which attains the smaller height is $........$

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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

Two particles $A$ and $B$ are moving in the $XY$ plane. Particle $A$ moves along a line with equation $y = x$,while particle $B$ moves along the $X$-axis such that their $X$-coordinates are always equal. If particle $B$ moves with a uniform speed of $3 \ m/s$,what is the speed of particle $A$?

$A$ block of mass $5\,kg$ is moving horizontally at a speed of $1.5\,m/s$. $A$ perpendicular force of $5\,N$ acts on it for $4\,s$. What will be the distance of the block from the point where the force started acting?

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is:

$A$ point traversed $3/4$th of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is

Two stones are projected so as to reach the same horizontal range on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then,the angle of projection of the stone which attains the smaller height is $........$

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