# Vectors components

## Homework Statement

a boat heads due east across a stream with a velocity of 20m/s. the stream is flowing from north to south at a rate of 5.0m/s.
a)What is the resultant velocity?
b) if the stream is 100 m wide, how much time does it take the boat to reach the other side?
c) How far downstream is the boat when it reaches the other side?

## The Attempt at a Solution

for the resultant, i just took pythagorean theorem to find out an answer of 20.6m/s. that angle I got by using tan inverse. which is 14.0 degrees

To get the time do i just take the 100m and divide it by the resultant velocity?
How do i find how far downstream the boat is when it reaches the other side?

## Answers and Replies

PhanthomJay
Science Advisor
Homework Helper
Gold Member
The magnitude of the resultant velocity looks ok. It's direction is 14 degrees from which axis? You would have to consider the diagonal distance to calculate the time it takes to reach the other side, when using the resultant velocity. It might be simpler to calculate the time to reach the other side and distance traveled downstream by considering the velocity components independently.

The magnitude of the resultant velocity looks ok. It's direction is 14 degrees from which axis? You would have to consider the diagonal distance to calculate the time it takes to reach the other side, when using the resultant velocity. It might be simpler to calculate the time to reach the other side and distance traveled downstream by considering the velocity components independently.

Its 14 degrees from the x axis. In the first quadrant.
I still don't understand how to calculate how far downstream the boat is when it reaches the other side?

PhanthomJay
Science Advisor
Homework Helper
Gold Member
Its 14 degrees from the x axis. In the first quadrant.
I still don't understand how to calculate how far downstream the boat is when it reaches the other side?
the boat is moving easterly but the current from north to south is causing it to drift downstream southerly. In which quadrant would its motion lie at 14 degrees from the x axis? Did you calculate the time it takes to reach the other side? Use that time to calculate the distance travelled downstream based on its downstream speed of the current.