Velocity of the Moon (magnitude and direction)

corykowa

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

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 = 0.200 days
______ m/s
______ degrees (counterclockwise from the +x axis)

(b) between t = 0 and t = 0.0020 days
_____ m/s
_____ degrees (counterclockwise from the +x axis)


3. The attempt at a solution

When I try to solve for Vx and Vy I get the same result for each one, yielding zero, and if I try another method, i get very minute numbers. None of which appear to be correct. I'm at a loss for how to do this problem

tiny-tim

Hi corykowa! Welcome to PF!

(on this forum, just use the bold (B) tag for vectors: v = v[−sin (ωt)i + cos (ωt)j] )
What formula did you use for average acceleration?

Show us what you tried, and then we'll know how to help!

corykowa

Hi thanks for the help. I was thinking since the moon is moving around us, that it would be a centripetal acceleration problem? But maybe that's where I was going wrong. So I was using that formula in relation to vectors...

a = -lim (v/2*theta)2vsin(theta)ey as lim of theta approaches zero = (-v^2/R)ey

tiny-tim

Hi corykowa!

(just got up …)
(have a theta: θ and try using the X² tag just above the Reply box )

No, you're misreading the question.

It's only asking you for the average acceleration.

(a), over 0.2 days, will give you a figure close to the instantaneous acceleration, and (b), over 0.002 days, will give you a figure even closer.

The formula you need is average acceleration = (v(t₂) - v(t₁))/(t₂ - t₁)

corykowa

Oh thank you much! I just tried that equation and my response "differs from the correct answer by orders of magnitude". I'm not too sure what that means... I feel like i must be off by 10^x in my answer but not too sure how to go about figuring that out?? I got 945 when t=2 and 1.89 when t=.002. Also, I still don't understand how to solve for the direction (in relation to the +x axis). I figure it has something to do with arctan?? Thank you!

tiny-tim

Hi corykowa!

(just got up …)
(try using the X² tag just above the Reply box )

Did you remember to convert the days into seconds?

Show us your full calculations, and then we'll see what went wrong, and we'll know how to help!

(and y/x is the tangent of the angle from the x-azis)

corykowa

I had completely spaced converting days into seconds. However, what I ended up doing was:

differentiate v(t) = v( -sin(wt) + cos(wt)) which is
-v(w) (cos(wt) + sin(wt)) you have the acceleration
v(w) = 2.32 x 10^-3 meter/sec^2
At t = 0 days, the acceleration is - 2.32 x 10^-3 meters/sec^2

This appears to be what my homework was asking me as webassign accepted this as correct.

I'm still in the process of figuring out the direction part though. I'm trying: [tex]\theta[/tex] = artan Vy/Vx

Thank you for your help!