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**1. Homework Statement**

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?

**2. Homework Equations**

f=ma

x=vt+1/2at^2

**3. 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