What is the Maximum Height the Sun Will Reach Above the Galactic Midplane?

[leonne]

Homework Statement

The Sun is presently about 20 pc out of the midplane of the disk, and moving
away from the midplane at about 7.4 km s−1. Using these as the current position,
z(tnow), and velocity, vz(tnow), what is the maximum height zmax (in pc) the Sun
will reach before turning around?

Homework Equations

z(t)=Asin(vt)
where z(t) is the vertical position of a test particle, A is the amplitude of its motion,
and t = 0 is the time when the particle is at the midplane

The Attempt at a Solution

Would I use this formula to solve this question, or something different? Any hints would be appreciated
thxs

 

[leonne]

ok after thinking about it , would i use v(t)=Avcos(vt) to find how long it will take for v final to =0 then plug in the time into the position z(t)=Asin(vt) than that will give me the max height? Also to find what A= i remember from my mechanics classes when we had a general solution to find what a= we set t=0 would i do the same here?