A ball is dropped from the roof of a building, and its height (in feet) is modeled by the functionf(t) = −16t2 + 80where t is measured in seconds. What is the speed of the ball exactly 4 seconds after it was dropped?

The ball’s velocity is the derivative of its height: f′(t) = −32t feet per second. At t = 4 seconds, its velocity is −32(4) = −128 ft/sec. Speed is the magnitude of velocity, so the ball’s speed is 128 ft/sec, choice A.

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