Question

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?

Answer 1

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