The distance an object falls (when released from rest, under the influence of Earth’s gravity, and with no air resistance) is given by d(t) = 16t², where d is measured in feet and t is measured in seconds. A rock climber sits on a ledge on a vertical wall and carefully observes the time it takes a small stone to fall from the ledge to the ground.

a. Compute d'(t). What units are associated with the derivative and what does it measure? Interpret the derivative.

b. If it takes 6 s for a stone to fall to the ground, how high is the ledge? How fast is the stone moving when it strikes the ground (in mi/hr)?