Problem 8. A small, dense probe is dropped from a stationary weather balloon to collect data while falling. The probe initially falls with a velocity (in meters per second (m/s)) given

by v(t) = 9.8t, this is because of the force of gravity after neglecting air resistance. After 10 seconds elapse, a chute deploys and the probe immediately slows to a constant speed of 10m/s, which the probe maintains until it enters the ocean. (a) Graph the velocity function. (b) How far does the probe fall in the first 30 seconds after it is released? (c) If the probe was released from an altitude of 3 kilometers, when does it enter the ocean?