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 6.2s 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 miles per​ hour)?

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