Two cyclists are moving from a junction of tw | vedclass

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(A) Let the position of the first cyclist be $A$ and the second cyclist be $B$ at time $t$. Let the distance between them be $x$.Given $OA = 4t$ and $

Vedclass · Accepted Answer

$\sqrt{37}$

Vedclass · Answer

(A) Let the position of the first cyclist be $A$ and the second cyclist be $B$ at time $t$. Let the distance between them be $x$.Given $OA = 4t$ and $OB = 3t$.Using the Law of Cosines in $	riangle OAB$:$x^2 = (OA)^2 + (OB)^2 - 2(OA)(OB) \cos(120^{\circ})$$x^2 = (4t)^2 + (3t)^2 - 2(4t)(3t) \left(-\frac{1}{2}ight)$$x^2 = 16t^2 + 9t^2 + 12t^2$$x^2 = 37t^2$$x = \sqrt{37}t$The rate at which they are separating is $\frac{dx}{dt}$.$\frac{dx}{dt} = \frac{d}{dt}(\sqrt{37}t) = \sqrt{37} 	ext{ km/h}$.

Two cyclists are moving from a junction of two roads inclined at an angle of $120^{\circ}$ to each other,with velocities of $4 \text{ km/h}$ and $3 \text{ km/h}$ respectively. The rate at which they are separating from each other after $1 \text{ hour}$ is ..... $\text{km/h}$.

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