A 30.0-kg object experiences a drag force due to air resistance with a magnitude proportional to the square of its speed. The object falls with an acceleration of 4.00 m/s2 downward when it is falling downward at 70.0 m/s. What is its terminal speed?

Drag force at 70 m/s:

F₁ = ma

F₁ = 30 x 4

= 120 Newtons

Drag force at terminal velocity:

No net force so drag = weight of object:

F₂ = mg

F₂ = 30 x 9.81

= 294.3 Newtons

We know that the force is proportional to the square of velocity:

F = kv²

F₁/v₁² = F₂/v₂²

v₂ = √ ((294.3 x 70²) / 120)

v₂ = 109.6 m/s