Circular Motion: Change in Height, Box Struck by Arrow

[MaZnFLiP]

Homework Statement

A box of mass 4.750Kg is suspended from a rope which is attached to the ceiling and is currently at rest. You then shoot an arrow horizontally with a velocity of 21.00 m/s toward the box while standing 4.5m away from it. You may neglect air resistance.

A. With what velocity will the arow strike the box?
B. If the arrow has a mass of 0.2500Kg, what is the max change in height the box theoretically will experience?

Homework Equations

b = Box, a = arrow

KEib + KEfb = KEia + KEfa

Fc = MV^2/r

Fg = mg

The Attempt at a Solution

So what I did was I first solved for the Final Velocity of the box which would become the new initial velocity after the arrow struck the box using the KEib + KEfb = KEia + KEfa.

0.5(4.750)V^2 = 0.5(0.25)(21.00)^2

Solving for the Velocity, I got 4.82m/s. so that becomes the new velocity I have and the New initial velocity would be 0. My New givens are:

Vi = 4.82m/s
Vf = 0m/s
A = -9.81m/s^2
$$\Delta$$y = ?

If I'm looking for the change in height, I don't feel like I need Centripetal Force. Would I just need to worry about $$\Delta$$y? or do I have to use the Centripetal force equation?

 

[Google_Spider]

KEib + KEfb = KEia + KEfa

and what about PE ??

 

[MaZnFLiP]

Oh! Haha I completely forgot. Thanks so much!