Question

A boat moves ar 10.0 m/s relative to

thewater. If the boat is in a river where the current is 2.00 m/s,
howlong does it take the boat to make a complete round trip of 1000
mupsteam followed by a 1000- m trip downstream?

Answer 1

Answer: 208.3 s

Step-by-step explanation:

Hi!

You need to calculate the velocity of the boat relative to the shore, in each trip.

Relative velocities are transformed according to:

`V_(b,s) = V_(b,w) + V_(w,s)\\ V_(b,s) = \text{velocity of boat relative to shore}\\V_(b,w) = \text{velocity of boat relative to water} \\V_(b,w) = \text{velocity of water relative to shore}\\`

Let's take the upstram direction as positive. Water flows downstream, so it's velocity relative to shore is negative , -2 m/s

In the upstream trip, velocity of boat relative to water is positive: 10m/s. But in the downstream trip it is negatoive: -10m/s

In upstream trip we have:

`V_(b,s) = (10 - 2)(m)/(s) = 8 ms`

In dowstream we have:

`V_(b,s) = (-10 - 2)(m)/(s) = -12 ms`

In both cases the distance travelled is 1000m. Then the time it takes the round trip is:

`T = T_(up) + T_(down) = (1000)/(8)s + (1000)/(12)s = 208.3 s`