# Environmental force vs. Drag force acting on an object: Calculating motion parameters

1. May 17, 2012

### Student1989

1. The problem statement, all variables and given/known data

An object is influenced by 2 forces: environmental force F1 = 42 tons and a hydrodynamic drag factor F2 = 200 kN. These forces are directed against each other (one attempting to 'weaken' the other one). The corresponding mass of object is 10,112 tonnes. I am trying to create a speed-time diagram - v(t) - showing the effect of the two forces on the movement of the object. Furthermore, I need to calculate the speed of the object upon reaching a distance of x metres (where x - any chosen distance).

2. Relevant equations

Limit velocity:
Vlim = √(V1/V2)

speed calculation:
m ⋅ ΔV = F ⋅ t
ΔV = (F1 ⋅ t) / m

acceleration vs. distance:
s = (a ⋅ t2)/2

others:
???

3. The attempt at a solution

for the environmental force (F1):
F1 = 42 [t] = 42 [t] ⋅ 9.81 [kg⋅m/s²] = 412.02 kN
Δ V1 = (412.02 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.041 ⋅ t [m/s]

for the drag force (F2):
F2 = 200 kN
Δ V2 = (200 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.020 ⋅ t [m/s]

I obtained two values of acceleration and velocity resulting from the two forces F1 and F2 separately. Since they have opposite directions, I tried to calculate as following:

t ⋅ (0.041-0.020)

I figured that it's wrong, because the velocity cannot go towards infinity (because of the drag force acting), rising only to the limit velocity:

Vlim = √(V1/V2) = √(0.041/0.020) ≈ 1,432 [m/s].

What mistake do I make in the calculation?