Question

A group of soldiers are marching with a speed of 5 m/s. The distance between the first and the last row of soldiers is 100 m. A dog starts running from the last row and moves towards the first row, turns and comes back to the last row. If the dog has travelled 400 m, the speed of the dog is:

• A. $5\sqrt{2}m/s$
• B. $3\sqrt{5}m/s$
• C. $6\sqrt{5}m/s$
• D. $6\sqrt{2}m/s$

Answer 1

The correct option is A $5\sqrt{2}m/s$

Assume speed of dog to be 's'
Then time taken by dog to catch up with soldier in first row = $\frac{100}{(s-5)}$
where 5 is the speed given of the soldiers.
Also the taken to move back from first soldier to last soldier = $\frac{100}{(s+5)}$
Now according to given conditions
$(\frac{100}{(s-5)}+\frac{100}{(s+5)})\times s=400$

Solving above eqaution, we get = $5\sqrt{2}.$
Hence, option (a) is correct answer.