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# Two Dimensional Motion Using Vectors

### #1

Posted 26 September 2010 - 07:13 PM

A river flows due east at 1.50 m/s. A boat crosses the river from the south bank to the north bank by maintaining a constant velocity of 10.0 m/s due north relative to the water.

a. What is the velocity of the boat as viewed by an observer on the south bank?

b. If the river is 325 m wide, how much time will it take for the boat to cross the river?

c. How far downstream is the boat when it reaches the north bank?

d. What is the boat's displacement?

e. What is the magnitude of the boat's displacement?

f. What is the boat's average speed?

My answers, work omitted.

a. 10.1 m/s NE

b. 32.2 seconds

c. 12.0 m

d. 325.22 m NE

e. 325.22 m at 87.8° North of East

f. 10.1 m/s

### #2

Posted 27 September 2010 - 09:31 PM

I missed much of my physics lecture on Friday, so I'm not entirely sure what I'm doing, and we have a homework quiz on this Monday. =/ If this seems really trivial.. it probably is, but I wasn't there to learn it (so don't judge me >_>). The homework is pretty much all reminiscent of this problem, so if I understand this, I should be clear. Check mah answerz pwease?

A river flows due east at 1.50 m/s. A boat crosses the river from the south bank to the north bank by maintaining a constant velocity of 10.0 m/s due north relative to the water.

a. What is the velocity of the boat as viewed by an observer on the south bank?

b. If the river is 325 m wide, how much time will it take for the boat to cross the river?

c. How far downstream is the boat when it reaches the north bank?

d. What is the boat's displacement?

e. What is the magnitude of the boat's displacement?

f. What is the boat's average speed?

My answers, work omitted.

a. 10.1 m/s NE

b. 32.2 seconds

c. 12.0 m

d. 325.22 m NE

e. 325.22 m at 87.8° North of East

f. 10.1 m/s

Maybe too late to help.

a. 10.1118.., so 10.1 looks good.

b. Use only the northward component of the boat's velocity, not [a], to compute this time = 32.5 sec.

c. Use 32.5 sec and the river's speed to get downstream distance.

d. displacement = ? 325m N + [c] E?

e. Angle east of North would be arc tan (river speed/boat speed) = tan

^{-1}(.15) = 8.53

^{o}f. Don't understand. It's constant at [a], so why ask for average?

Good luck.

- bn

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 28 September 2010 - 04:46 AM

NE is not entirely descriptive as it implies 45 deg north of east, which is not the actual direction.

You can also determine the magnitude and the exact angle.

The magnitude should also be the answer for (f)

Either of the two approaches will be correct.

I concur with bonanova for (b) and ©

For (d)

They are asking for a vector here, and you can choose either cartesian or polar forms.

I think your answer will change if you change (b).

(e) is just the magnitude of the (d) vector.

(f) is just the magnitude of the (a) vector

**Edited by mmiguel1, 28 September 2010 - 04:49 AM.**

### #4

Posted 29 September 2010 - 10:00 PM

One of my friends helped me the morning before the quiz and we compared homework answers, and I was good in the end. (..After serious revision. >_>)

**Edited by Izzy, 29 September 2010 - 10:00 PM.**

### #5

Posted 13 June 2012 - 04:38 AM

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