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*root2m/ s

(b) 3*root5m/ s

(c) 6*root5m/ s

(d) 6*root2m/ s

Answer 1

Given:

Group of soldiers are marching with a speed of 5 meters per second.

Distance between first and last row of soldiers is 100 meters.

A dog starts running from last row to first and turns back to the last row.

Total distance traveled by dog is 400 meters.

To Find:

The speed of the Dog ?

Solution:

Let the actual speed of dog is v.

Relative speed of dog when dog moves from last row to first row = v - 5

distance traveled= 100 m

Let time taken by dog to run from last row to first row is t.

$Speed = \frac{Distance}{time} \\\\ v-5 = \frac{100}{t}$ (1)

Relative  Speed of dog when dog moves from first row to last row = v + 5

distance traveled = 100 m

Let time taken by dog to run from first row to last row is T.

$v + 5 = \frac{100}{T}$      (2)

Total distance traveled by dog = 400 m

speed = v

total time = t + T

$v = \frac{400}{t+T}$

substitute t and T from 1st and 2nd equation;

$t = \frac{100}{v-5} \\T= \frac{100}{v+5}$

$v = \frac{400}{\frac{100}{v-5} + \frac{100}{v+5} } \\take LCM.\\2(v-5)(v+5) = v^{2}\\ v =\sqrt{50}\\ v = 5\sqrt{2}$

v = $5\sqrt{2} \frac{m}{s}$

The speed of dog is $5\sqrt{2} \frac{m}{s}$.