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Standard XII

Mathematics

Average Rate of Change

Two cyclist s...

Question

Two cyclist start from the junction of two perpendicular roads, their velocities being $3 v$ metres/minute and $4 v$ metres/minute . The rate at which the two cyclists are separating is

\frac{7}{2} v

m/min

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5 v

m/min

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v

m/min

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none of these

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Solution

The correct option is B $5 v$ m/min
The cyclist will be separating along the vector sum of the perpendicular velocity vectors of the two cyclists, since their speeds are constant.
Hence they will be separating at the rate
$\sqrt{(3 v)^{2} + (4 v)^{2}} .$
$= 5 v m / m i n$

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Two cyclist start from the junction of two perpendicular roads, their velocities being 3v metres/minute and 4v metres/minute . The rate at which the two cyclists are separating is

The correct option is B 5v m/minThe cyclist will be separating along the vector sum of the perpendicular velocity vectors of the two cyclists, since their speeds are constant.Hence they will be separating at the rate √(3v)2+(4v)2.=5vm/min

Two cyclist start from the junction of two perpendicular roads, their velocities being $3 v$ metres/minute and $4 v$ metres/minute . The rate at which the two cyclists are separating is

The correct option is B $5 v$ m/min
The cyclist will be separating along the vector sum of the perpendicular velocity vectors of the two cyclists, since their speeds are constant.
Hence they will be separating at the rate
$\sqrt{(3 v)^{2} + (4 v)^{2}} .$
$= 5 v m / m i n$