Question

During the shooting of a super hit 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 30 km/h and each of them walked at 4 km/h, starting 400 m apart?
A. 400 m
B. 880 m
C. 1500 m
D. 30 km

Answer 1

Hint: It is said that Amitabh Bachchan was waiting for Amrita Singh along with his dog. When she arrives the dog gets excited and starts to run from one person to another. Thus the dog continues running till both of them meet. We are given the speed of the dog, Amitabh Bachchan and Amrita Singh and also the initial distance between Amitabh Bachchan and Amrita Singh. In this question all the three bodies are moving. To find the total distance covered by the dog, first we need to find the time taken by Amitabh Bachchan and Amrita Singh to meet by making one the frame of reference. This is the time taken by the dog to cover the total distance. Since we are given the speed of the dog, by using the time we can find the distance covered by the dog.
Formula used:
$\text{speed=}\dfrac{\text{distance}}{\text{time}}$

Complete answer:
In the question it is said that Amitabh Bachchan is waiting with his dog for Amrita Singh.
It is said that when Amrita Singh approaches them, the dog gets excited and starts to run towards Amrita and back to Amitabh.
Initially they are at a distance of 400 m.
The dog runs towards Amrita and back to Amitabh with a speed of 30 km/hr.
It is also said that Amitabh and Amrita walk towards each other with a speed of 4 km/hr.

The given situation is depicted in the figure above.

From the question we can understand that the dog keeps running until Amitabh and Amrita meet each other.
Therefore let us find the taken for Amitabh and Amrita to meet.
For that let us consider Amitabh as the frame of reference.
Therefore we know that we can consider Amitabh in rest.
Hence the velocity of Amitabh will be acquired by Amrita, thus the velocity of Amrita will become 8 km/hr.
Therefore we can say that, Amitabh will be at rest and Amrita is approaching Amitabh with a speed of 8 km/hr.
Therefore we can find time taken by Amrita to reach Amitabh.
We know that,
$\text{speed=}\dfrac{\text{distance}}{\text{time}}$
Therefore, $\text{time=}\dfrac{\text{distance}}{\text{speed}}$
Here,
$\text{Distance}=400m=400\times {{10}^{-3}}km$
Speed = 8 km/hr
Therefore,
$\begin{align}
  & time=\dfrac{400\times {{10}^{-3}}}{8} \\
 & time=0.05hrs \\
\end{align}$
This is the time taken for Amitabh and Amrita to meet.
Therefore, we can also say that the dog will run from Amitabh to Amrita for 0.05 hrs.
Hence we can find the distance traveled by dog using the same equation.
$\text{speed=}\dfrac{\text{distance}}{\text{time}}$
Therefore,
$\text{distance=speed }\!\!\times\!\!\text{ time}$
We know the speed of the dog is 30 km/hr and the time we found earlier to be 0.05 hrs.
Therefore,
$\text{distance}=30\times 0.05$
$\text{distance}=1.5km=1500m$
Therefore the distance traveled by the dog is 1500 m.

So, the correct answer is “Option C”.

Note:
When two bodies are moving relative to each other, we can fix one of the bodies as the frame of reference. When we do so, that body taken as the frame of reference will be considered to be at rest. The velocity of that body will be added relatively to the other body.

In this case, since Amitabh is moving in the positive x direction and Amrita is moving in the negative x direction, the velocity of Amitabh will be added to the velocity of Amrita when we consider Amitabh to be the frame of reference.