Question

A boat moves ar 10.0 m/s relative to

Answer 1

Answer: 208.3 s

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:

$V_{b,s} = (10 - 2)\frac{m}{s} = 8 ms$

In dowstream we have:

$V_{b,s} = (-10 - 2)\frac{m}{s} = -12 ms$

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

$T = T_{up} + T_{down} = \frac{1000}{8}s + \frac{1000}{12}s = 208.3 s$