How coordinate system choice affects tension force calculations

[Amideus]

Homework Statement

Homework Equations

F=ma
vi=vf + at

The Attempt at a Solution

If i was to define upward as positive y direction, would the answer be = -881 pounds (btw why is the answer in the image in Newtons?) and because i defined upward as +y would
ƩF = T - w? where w = mg.

 

[briantaekim]

I think you are right about the units. I am not too familiar with slugs, pounds, ft/s^2 but I think you're right about Newtons being a typo.

On the other hand, you are wrong about the direction of the force. Since we set upward as positive, the initial and final velocities are negative.

a=(V_f-V_i)/t=(-35-(160))/0.80=+156 ft/s^2

Since the acceleration is upward, the retarding force is also upward.