# Direction and velocity vector problem

1. May 10, 2014

### timnswede

1. The problem statement, all variables and given/known data
At one instant a bicyclist is 60 m due east of a park’s flagpole, going south at 20 m/s. Then 30 s later, the cyclist is 40 m due north of the flagpole, going due east with a speed of 10 m/s. On an XY-coordinate system with the flagpole at the origin, for the cyclist in this 30 s time interval:
a.) Draw position and velocity vectors as described
b.) Obtain displacement vector in unit-vector notation
c.) Obtain average velocity vector in unit-vector notation
d.) Obtain average acceleration vector in unit-vector notation
e.) Draw the vectors found

2. The attempt at a solution
a.) I was kind of confused on this part for a bit, but the position and velocity vectors are completely separate right? For position I drew the first one 60m straight east and from that vector one straight up 40m. Same idea for the velocity vectors.

b.) I'm not sure about this but I did final - initial, so (0i+40j) -(60i+0j) = -60i + 40j

c.) Displacement over time so (-60i+40j)/30s = -2i+4/3j

d.) Vf-Vi/t so (10i+0j)-(0i-20j)= (10i+20j)/30s = 1/3i + 2/3j

e.) I just drew all the vectors I found.

2. May 10, 2014

### paisiello2

a) I would draw the position vector from the same datum point i.e. the flagpole. Don't continue it off from another vector's end point. Velocity vector's would always be drawn from the end point of the position vector i.e. the datum point 's coordinates change in this case.

b) Looks correct.

c) Looks correct.

d) Looks correct.

3. May 11, 2014

### Curieuse

Yes. paisiello2 said it about the velocity vectors! And I recognize this to be from Halliday and Resnick only they asked about the magnitudes and directions of the displacement, avg velocity and avg acceleration and not any graphical vector representation! But to enhance it, I attached a drawing! Hope it helps as well.

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