Question

Two men A and B start with velocities v at the same time from the junction of two roads inclined 45 degrees to each other if they travel by different road the rate at which they are being separated​

Answer 1

At the rate of 0.76v A and B are being separated.

Step-by-step explanation:

See the attached diagram.

Let the two roads are AB and AC which are inclined to each other at 45°.

Now, as the two men A and B are moving along AB and AC with the same velocity, so at any instance, their distances from point A will be equal.

So, consider Δ ABC as an isosceles triangle and draw perpendicular on BC from vertex A i.e. AD which is the bisector of side BC.

Now, from the right triangle Δ ADC,

$\sin 22.5^{\circ} = \frac{\frac{x}{2} }{d}$

⇒ x = 0.76d

Now, differentiating with respect to time (t) we get,

$\frac{dx}{dt} = 0.76v$

Therefore, at the rate of 0.76v A and B are being separated. (Answer)

Answer 2

Answer:

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