Question

PLZ HELP!!!!!!
6. A boat is traveling west across a river. The river is 400.0m wide and the speedometer reading on the boat is 30.0 km/hr. The current in the river is flowing south at 5km/hr. The boat driver is not compensating the current. c) How far downstream did the boat travel? d) What was the total distance traveled by the boat?

Answer 1

You didn't state what you need to find, but it looks like you need to find the component of the velocity along the width of the river. If the width of the river is in the x direction flow of the river is in the y direction, the resultant velocity will be \[v ^{2}=v _{x}^{2}+v _{y}^{2}\]where v is the resultant velocity; vx is the velocity in the x direction; and vy is the velocity in the y direction. You should be able to use that to find vx.

Answer 2

@PsiSquared
Since the speedometer is measured relative to the water, and the boat is only moving west relative to the water it's in (ideally), wouldn't the velocity across the river be \(30\ \rm km/hr\)?
In your scenario, \(v_x=30\ \rm km/hr\) and is thus known?
The downstream velocity would be \(v_y=5\ \rm km/hr\), as given.
Then \(\vec v=(v_x,~v_y)\) would be unknown.

But the question might have changed in that content anyway, since the questions were not posted at the time you responded.

@aminehr
I'd look into how long it'd take to cross the river, basic \(v=\dfrac{\Delta d}{\Delta t}\).
Then see how far downstream you'd go in that time. Same equation!

To find the total distance, you'll want to use the Pythagorean theorem using the river width and downstream travel distance. Here's why: