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.