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Question

Answers

$

(a){\text{ 400m}} \\

(b){\text{ 880m}} \\

(c){\text{ 1500m}} \\

(d){\text{ 30m}} \\

$

Answer

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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.

Complete step-by-step 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.

Complete step-by-step 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.

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