# Homework Help: Calculating Magnitude and Vector Componends given Momentum and Mass

1. Oct 15, 2011

### zboomer

Hi =) just signed up, and i really need help this term. im really having a hard time this term absorbing whats going on, im getting things mixed up, and im falling behind.. im finding myself quickly losing my confidence and becoming quite frustrated and stressed out ;( im really sorry to open up that way but =) its good to be here, i'll probably be here quite frequently.. i appreciate all patience with me..

1. The problem statement, all variables and given/known data
"A 2.0kg object's momentum at a certain time is 10kg.m/s 37° vertically upward from due west. What are the components and magnitude of its velocity at this time (in a frame in standard orientation)?"

2. Relevant equations
p=mv
v=dr/dt
mag(v)=√((dx)^2 + (dy)^2 +(dz)^2)
a^2 + b^2 = c^2

3. The attempt at a solution
im not getting very far but heres where im at:

first i plug what i know into the formula for momentum.

10kg.m/s = 2kg.v

i divide 10kg.m/s by 2kg (canceling out my kg units) leaving me with a velocity of 5m.s

i understand that if i draw a picture, i basically am looking at an object that is rising at a rate of 5m.s 37° west of my position. whats really killin me is that i cant figure out how to go backwards to find any distances to go with to figure out my magnitude, or even the actual time to divide those distances from ;\

what i have done is since i havnt been given a time interval, i plugged 5 for my dr, and used 1 second for dt

since i had a distance of 5 meters:

5tan(37°) = -3.767770251m x-hat for my adj. (the ground), and i used the Pythagorean theorem to find a hypotenuse. i know im just slaughtering the terminology..

a^2 + b^2 = c^2
√((5)^2 + (-3.767770251)^2) = 6.260678291m

i didnt know what to do from here to satisfy my dr portion so i used C as my dr so i could divide by my velocity (5m.s) to find a more accurate time interval to finish things off with

6.260678291m / 5m.s

t = 1.252135658seconds

canceling out the meters im left with

i then used this to find my final magnitude

mag(v) = √(((5)^2 + (-3.767770251)^2 + (6.260678291)^2) / t)
mag(v) = 7.912444813

with my final components being
x - -3.767770251m x-hat
y - 6.260678291m y-hat
z - 5m z-hat

i know i skillfully messed this problem up early.. and im sorry if the way i spewed this all out is not very conducive or easy to follow.. im really struggling here ;\

zboomer

2. Oct 15, 2011

### zboomer

sorry that final column vector probably should have read

x - -3.767770251m x-hat
y - 5m y-hat
z - 6.260678291m z-hat