River and boat velocity problem

[akbro93704]

Homework Statement

(1) A River flows due east at 1.20 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water. I got the velocity of the boat relative to shore at 9.08 m/s at 82.406 degrees north of east. What about if the river is 380m wide, how far downstream has the boat moved by the time it reaches the north shore?

Homework Equations

The Attempt at a Solution

I got the velocity by setting up components and using the Pythagorean theorem and tangent. What do I do with the 380m to figure out how far downstream the boat has moved by the time it reaches north shore? thanks

 

[Redbelly98]

How long does it take for the boat to cross the river?

 

[baba89]

Based on the given information, we can use the formula d = rt to calculate the distance traveled by the boat downstream. The distance (d) is equal to the rate (r) multiplied by the time (t). In this case, the rate is the velocity of the boat relative to the shore, which is 9.08 m/s. The time can be calculated by dividing the width of the river (380m) by the velocity of the boat relative to the water (9 m/s), which gives us a time of approximately 42.22 seconds. Therefore, the distance traveled downstream by the boat is 9.08 m/s x 42.22 s = 383.55 m. This means that by the time the boat reaches the north shore, it would have traveled approximately 383.55 meters downstream.