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
