Newtonian - Force, Gravity, and Bungee Jumping

[staycrunchy]

Homework Statement

A person weighing 55kg jumps off of a bridge with a bungee cord attached. The problem seeks to find the bungee cords Force vector when the acceleration is 7.8m/s² in the downward direction.

m = 55kg
a₁ = g = 9.8m/s²

To find:
F₁ when a₂ = 7.8m/s² downward.

I've specified my grid as $$\uparrow$$+ $$\rightarrow$$+ so the accelerations are technically negative.

Homework Equations

$$\Sigma$$F = ma

The Attempt at a Solution

$$\Sigma$$F = ma
$$\Sigma$$F=55kg(-7.8m/s²)
$$\Sigma$$F = -418N

$$\Sigma$$F = F₁ - F₂
$$\Sigma$$F = 539N - 418N
Force of bungee cord acting = +121N

 

[semc]

Why did you subtract the forces?

 

[staycrunchy]

Why did you subtract the forces?

The 539N was the Force with F=ma and a = g. I think I forgot to write that.
The -428N was the Force with F=ma and a = 7.8m/s².

My inclination was to subtract the forces to get the force required by the bungee cord to slow the decent to the 7.8m/s²

 

[semc]

Well since gravitational force is downwards and he is traveling downwards...