# Velocity of the Moon

1. Jan 15, 2010

### planke

1. The problem statement, all variables and given/known data

The velocity of the Moon relative to the center of the Earth can be approximated by varrowbold(t) = v [−sin (ωt) xhatbold + cos (ωt) yhatbold], where v = 945 m/s and ω = 2.46 multiplied by 10−6 radians/s. (The time required for the Moon to complete one orbit is 29.5 days.) To approximate the instantaneous acceleration of the Moon at t = 0, calculate the magnitude and direction of the average acceleration during the following two time intervals.

(a) between t = 0 and t = 0.400 days
______ m/s
______ degrees (counterclockwise from the +x axis)

(b) between t = 0 and t = 0.0040 days
_____ m/s
_____ degrees (counterclockwise from the +x axis)

2. Relevant equations
aav = delta v / delta t
ax = delta vx / delta t
ay = delta vy / delta t
magnitude = sqroot (ay^2 + ax^2)
theta = tan-1 (ay / ax)

3. The attempt at a solution

I got the magnitudes of both at 0.00233 m/s. I am having trouble finding the directions though.

I just used ax = delta vx / delta t and ay = delta vy / delta t to find the values of ax and ay, then I subbed these numbers into this eqn: magnitude = sqroot (ay^2 + ax^2). My answer for the direction in part (a) was 2.43558 degrees... which is wrong. Can anyone think of a better way to do this problem?

2. Jan 15, 2010

### ideasrule

Why did you calculate acceleration? You're supposed to calculate velocity. Theta would be the inverse tan of Vy/Vx.