A particle of mass 2.00 kg moves under a force given by
F~ = −(8.00 N/m)(xˆi + yˆj)
whereˆi and ˆj are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity~v = (3.00 m/s)ˆi + (4.00 m/s)ˆj.
a. After how much time will the particle ﬁrst return to the origin?
b. What is the maximum distance between the particle and the origin?
The Attempt at a Solution
Using f=ma, i find the acceleration to be a=-4x i + -4y j
Using x=vt+1/2at^2, if i set x as 0
So i get 0=3t+1/2(-4x)t^2 and 0=4t+1/2(-4y)t^2
I solve those 2 equtaions to get 3y=4x
but i don't know where to continue