Height estimate 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 for 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?
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)?
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