# Finding magnitude direction and speed of a plane trip

1. May 29, 2012

### wbetting

1. The problem statement, all variables and given/known data
A plane flies 425 km east from city A to city B in 40.0 min and then 954 km south from city B to city C in 1.70 h. For the total trip, what are the (a) magnitude (in km) and (b) direction of the plane's displacement, the (c) magnitude (in km/h) and (d) direction of its average velocity, and (e) its average speed (in km/h)? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east).

2. Relevant equations

magnitude is sqrt of a^2+b^2
direction is tan inverse of ay/ax

3. The attempt at a solution
ok so i found magnitude and direction and got parts a and b, c,e right but got part d, wrong and i think its because of a mathematical mistake but its driving me nuts! i got 1044.39 km for a and -65.987 degrees for b. for c i found velocity avg for x and y for avg velocity of x i did (425km/.666hr)= 637.5 km/h
for avg velocity y i did (954km/1.7 hr)= 384.71 km/hr
for d i did sqrt 637^2+384.71^2= 434.33 km/hr
i can't figure out what i did wrong on d i did inverse tan of -434.33/637.5 and keep getting -34.26 and at one point got -31.11. whattt am i doing wrong?!!

2. May 30, 2012

### Infinitum

Hi wbetting!

For part (d) you found the tan for the average velocities over different time intervals. That's why you get the wrong answer. But what is the actual direction of velocity? (Hint:defining velocity in terms of displacement will help)