Question

Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45° to each other. If they travel by different roads, find the rate at which they are being separated.

Answer 1

Given: two men A and B start with velocities v at the same time from the junction of the two roads inclined at 45° to each other

To find the rate at which they are being separated

Explanation:

Let A and B move a distance of x on different roads as shown above, there distance at any time t will be same as they have same velocity.

Hence

Now consider ΔAOB, applying the cosine rule, we get

y² = x²+x²-2x.x.cos 45°

Now multiplying and dividing by √2, we get

Now applying the derivative with respect to t, we get

Hence this is the rate at which the two roads are being separated.