Solve 2D Vectors Problem: Ferry Boat Crosses River

[jen333]

Hey everyone,
i have a question here on 2D problems that I'm pretty much stuck on

A ferry boat has a speed of 9.0km/h in calm water. Its pilot takes it on a heading due north across a river that has a current of 4.0km/h west. It takes 15 minutes to cross the river.
a) how far downstream does the ferry land? (the answer is 1.0km)


for a, (i've drawn a diagram) I've found the width of the river which is 2.3km and I've also found the velocity of the boat relative to the shore which is 9.8 km/h, 24 degrees W of N. from there, I'm stuck.

please help! TY!

 

[whozum]

You don't need the widht of the river. All you need to know is that he was crossing for 15 minutes, and that the current was 4km west.

This is enough to find out how far he drifted during the cross.

 

[jen333]

oooo...hehehe, i feel sort of silly after just calculating that.
thank you.
but i have one more question, just wondering: why doesn't the boat's 9.0km/h affect how far the boat lands? wouldn't that impact the angle in which the boat is going across the river along with the 4.0km/h?
i hope you understand what I'm trying to say...

 

[Hippo]

The ferryman maintains a strictly northward heading.

Thus, his velocity North will compound with but will not affect his velocity West. The velocities are at 90 degrees to one another. You see?


Think of it this way. West is the direction down the x-axis (left, and into the negative numbers), while North is the direction up the y-axis.
This allows us to use vector notation.

$$\vec v = [-4.0 \frac{km}{h}, 9.00 \frac{km}{h}]$$

The x and y components (or i and j, as they're often called) are separate.

 

[jen333]

YES! totally makes sense to me
Thx for the help!
jen