Distance and displacement, relative motion

[dance_sg]

1. The driver of a motor boat points it directly toward the opposite bank of a 52 m wide river. The speed of the boat is 4.0 m/s and the river flows at 3.2 m/s. When the boat reaches the opposite riverbank, what is the distance downstream from its point of departure?



2. d=df-di, Sine, Cosine, Tangent



3. i drew this out and found that 4.0m/s was my hypoteneuse, 3.2m/s was the x axis, and 52m is the y axis. I don't know where to go from here

 

[RoyalCat]

You can't quite make a triangle of quantities that have different units. Would you be comfortable comparing masses with velocities?

Just as with your previous question, the key here is vector addition.
For the sake of simplicity, we'll assume the river flows from west to east, and that the driver is on the south bank, pointing north.

You have a certain velocity for the boat going from south to east, and a certain velocity for the river pulling the boat down-stream.

How long will it take it to reach the other bank, given its south-north velocity, and what will its offset be by the time it reaches the other bank?

 

[dance_sg]

so does that mean i have to find the angles of one triangle first in order to find the answer ?

 

[RoyalCat]

so does that mean i have to find the angles of one triangle first in order to find the answer ?

Nope, that's irrelevant since the two velocities are orthogonal. The south-north motion is at a known constant velocity, as is the east-west motion. So you only need to know how long it takes the boat to reach the other bank, and how much the river pulls it in the current during that time.