Relative Velocity

Classical Mechanics Level 1

A boat while traveling upstream goes from point B to point A in 8 minutes and while traveling downstream goes from point A to point B in 4 minutes. What is the speed of the boat and the speed of the stream in kmph ?It can be assumed that the distance the boat covers while going from Point A to Point B on the stream is the same as the distance the boat takes to go from Point B to Point A. Both these distances are equal to 160 meters.

5, 0 kmph 1.8,0.6 kmph 5, 3 kmph 30, 10 kmph

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Mike Davison
Oct 17, 2017

I calculated a different answer.

First, calculate the total velocity in each direction before considering the stream:

Upstream, 0.15km in 1/12hrs

0.15 ÷ 1/12 = 1.8km/h

Downstream, 0.15km in 1/20hrs

0.15 ÷ 1/20 = 3km/h

Average these to get the actual velocity of the boat: (1.8+3) / 2 = 2.4km/h

Velocity of stream is therefore 0.6km/h

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Srinivasa Gopal
Oct 16, 2017

Let the velocity of the boat be b and that of the stream be s. So let the distance between A and B be d

While going upstream the relative velocity of the boat wrt a stationary point on the shore is equal to b - s and while going downstream the relative velocity of the boat with respect to a stationary point on the shore is b + s

So we have (160/(b - s )) = 8 (160/(b+s)) = 4

b - s = 20 b + s = 40

b = 30 meters/minute or 1.8 ; kmph s = 10 meters/minute or 0.6 kmph

0 Helpful 0 Interesting 0 Brilliant 0 Confused

There's a big error here:

You've given b = 30 meters / minute. This is actually the total velocity of the upstream trip. 150m / 30m per min = 5min

Mike Davison - 3 years, 7 months ago

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