According to one model that takes into account air resistance, the acceleration a(t) (in m/s²) of a skydiver of mass m in free-fall satisfies

where v(t) is velocity (negative since the object is falling) and k is a constant. Suppose that m = 75 kg and k = 0.24 kg/m.

(a) What is the skydiver’s velocity when a(t) = −4.9?

(b) What is the skydiver’s velocity when a(t) = 0? (This velocity is the terminal velocity, the velocity attained when air resistance balances gravity and the skydiver falls at a constant speed.)

Transcribed Image Text:

k a(t) = -9.8+v(t)² m