(A) Let the boy at $A$ be at the origin $(0, 0)$ and the boy at $B$ be at $(x, 0)$.The boy at $B$ moves along the $y$-axis with velocity $v_1$. His po

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(A) Let the boy at $A$ be at the origin $(0, 0)$ and the boy at $B$ be at $(x, 0)$.The boy at $B$ moves along the $y$-axis with velocity $v_1$. His position at time $t$ is $(x, v_1 t)$.The boy at $A$ moves with velocity $v$ to meet the boy at $B$ at time $t$. His position at time $t$ is $(v_x t, v_y t)$ such that $\sqrt{(v_x t)^2 + (v_y t)^2} = vt$.Since they meet at $(x, v_1 t)$,we have $v_x t = x$ and $v_y t = v_1 t$.Using the velocity magnitude condition: $(v_x t)^2 + (v_y t)^2 = (vt)^2$.Substituting the values: $x^2 + (v_1 t)^2 = v^2 t^2$.Rearranging for $t^2$: $v^2 t^2 - v_1^2 t^2 = x^2$.$t^2 (v^2 - v_1^2) = x^2$.$t = \frac{x}{\sqrt{v^2 - v_1^2}}$.

Class 11 Physics 3-2.Motion in Plane Relative Velocity (river boat, rain, wind)

Medium

Two boys are standing at points $A$ and $B$ on the ground,where distance $AB = x$. The boy at $B$ starts running perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and meets the other boy in time $t$. The value of $t$ is:

MHT CET 2025 All MHT CET

A
$\frac{x}{\sqrt{v^2 - v_1^2}}$
B
$\frac{x}{\sqrt{v_1^2 - v^2}}$
C
$\frac{x}{v - v_1}$
D
$\frac{x}{v + v_1}$

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

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$A$ man is crossing a river flowing with a velocity of $5\, m/s$. He reaches a point directly across at a distance of $60\, m$ in $5\, s$. His velocity in still water should be ........ $m/s$.

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$A$ man swimming downstream overtakes a float at a point $M$. After travelling a distance $D$,he turns back and passes the float at a distance of $D/2$ from the point $M$. The ratio of the speed of the swimmer with respect to still water $(v_s)$ to the speed of the river $(v_r)$ is:

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Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

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Two cars,at a certain instant,are $50 \ km$ apart on a line running from south to north. The one farther north is moving west at $25 \ km/hr$. The other is moving towards north at $25 \ km/hr$. How long do they take to reach their distance of closest approach (in $min$)?

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$A$ glass windscreen,whose inclination with the vertical can be changed,is mounted on a car. The car moves horizontally with a speed of $2\,m/s$. At what angle $\alpha$ with the vertical should the windscreen be placed so that the rain drops falling vertically downwards with velocity $6\,m/s$ strike the windscreen perpendicularly?

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Two boys are standing at points $A$ and $B$ on the ground,where distance $AB = x$. The boy at $B$ starts running perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and meets the other boy in time $t$. The value of $t$ is:

Similar Questions

$A$ man is crossing a river flowing with a velocity of $5\, m/s$. He reaches a point directly across at a distance of $60\, m$ in $5\, s$. His velocity in still water should be ........ $m/s$.

$A$ man swimming downstream overtakes a float at a point $M$. After travelling a distance $D$,he turns back and passes the float at a distance of $D/2$ from the point $M$. The ratio of the speed of the swimmer with respect to still water $(v_s)$ to the speed of the river $(v_r)$ is:

Two cars,at a certain instant,are $50 \ km$ apart on a line running from south to north. The one farther north is moving west at $25 \ km/hr$. The other is moving towards north at $25 \ km/hr$. How long do they take to reach their distance of closest approach (in $min$)?

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