QUESTION

# During the shooting of a superhot film ‘MARD’ Amitabh Bachchan was waiting for his beloved Amrita Singh with his dog. When he saw her approaching, the dog was excited and dashed into her then went back to master and so on, never stopping. How far would you estimate the dog ran, if its speed is 30km/h and each of them walked at 4km/h, starting 400m apart?$(a){\text{ 400m}} \\ (b){\text{ 880m}} \\ (c){\text{ 1500m}} \\ (d){\text{ 30m}} \\$

Hint – In this question the relative speed of Amitabh Bachchan walking towards Amrita Singh will be (4+4 = 8km/hr). Use the relation between distance, speed and time to get the answer.

Amitabh Bachchan and Amrita Singh walked to each other with a speed of 4 km/hr.
Therefore, the relative speed ${V_r}$ of Amitabh Bachchan and Amrita Singh is
${V_r}$= (4 + 4) km/hr. (‘+’ sign is because they walked to each other so the relative speed increases).
Now the distance between them is 400 meter.
So ${D_{{\text{relative}}}}$ = 400 meter.
As we know 1000 meter = 1 km.
Therefore, 400 meter = (400 / 1000) = 0.4 km
As we know distance, speed and time is related as
${\text{Distance = Speed }} \times {\text{ Time}}$
Therefore, the time (t) when they meet to each other is,
t = (relative distance / relative speed)
t = (0.4 / 8) = 0.05 hr.
The speed of a dog is 30 km / hr.
So the distance (S) travel by dog is
S = $30 \times 0.05$= 1.5 km.
And we all know 1 km =1000 meter.
Therefore, 1.5 km = 1500 meter.
So the dog traveled 1500 meter.
So this is the required answer.
Hence option (C) is correct.

Note – In the concept of relative frame, we make one person stationary and give its speed to another person. The key point is regarding the sign (either positive or negative), always remember that the speed of the person who is made stationary is given in the opposite direction to the other person.