Swimmer and Two Dimensional Equations

[wolves5]

A river 550 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.

a) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?
d1= ?

b) If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight across, as in part (a)), how far downstream is she swept before reaching the opposite bank?
d2 = ?

c) For the conditions of part (b), how long does it take for her to reach the opposite bank?

For this question, I just don't know how to start it. I mean there's no angles. I'm confused because I feel there's not much information like time and all that. I guess I just don't know how to approach this.

 

[ideasrule]

Hey wolves! No worries; I'll help you get started.

A river 550 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.

a) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?

Imagine you were the woman, and trying to swim across. How long does it take? You'll be moving along with the water, but that doesn't matter; the river's width doesn't change, so you'll cross in the same amount of time as if the water were still.

You're now an observer on the shore, watching the woman. How far does the water carry her in the time it takes her to reach the other side?

b) If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight across, as in part (a)), how far downstream is she swept before reaching the opposite bank?

This is getting a bit more complicated, so you might want to draw a vector diagram of the swimmer's velocity. Then use the same strategy as before: find her velocity perpendicular to the bank, and use that to find how long it takes her to cross. Find her velocity parallel to the bank, and use both that and the time you found to determine how far the river carries her.

 

[wolves5]

So for part a, I am using d=vit + 0.5at^2. So, 8(137.5) + 0.5(-9.8)(137.5^2). Is this right? Am I using the right equation?

 

[ideasrule]

No, because there's no acceleration, and gravity doesn't come into play in this question. Just d=vi*t is all you need.

 

[wolves5]

Ok so I got that one down. Now, i don't get part b. What did you mean?

 

[ideasrule]

If she's swimming at 4ft/s at a 37 degree angle, what's the component of her velocity in the direction perpendicular to the bank? How about the component parallel? (Hint: use sine and cosine)

 

[wolves5]

Ok. So, 4sin(37)=2.407 and 4 cos(37)=3.195. Then, I used these velocities and plugged it into D=vt. I used 137.5 as my time. It's still not the right answer.