(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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$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

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$A$ ball is dropped from a height of $49\,m$. The wind is blowing horizontally. Due to wind,a constant horizontal acceleration is provided to the ball. Choose the correct statement$(s)$. (Take $g = 9.8\,m/s^2$)

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$A$ particle moving in $x-y$ plane starts from the origin at $t=0$ with an initial velocity $(-\hat{i}+\hat{j}) \,ms^{-1}$ and undergoes an acceleration of $(6 \hat{i}+4 \hat{j}) \,ms^{-2}$. Its displacement after $2 \,s$ is (in $\,m$)

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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

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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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$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

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