ExamplesAt timet=0, a diver jumps from a diving board that is 32 feet high.The position of the diver is given bys(t) =-16t2+16t+32, wheres(t)is measured in feet andtis measured in seconds.a)When does the diver hit the water?

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Examplesb)What is the diver’s velocity at impact?

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Examplesc)What is the diver’s acceleration at any timet?

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ExamplesA ball is thrown vertically upward from the ground with an initial velocityof 64 ft/sec. If the positive direction of the distance from its startingpoint is upwards, the equation of motion iss(t) =-16t2+64t. Lettseconds be the time that has elapsed since the ball was thrown andsfeet be the distance of the ball from the starting point attseconds.a)Find the instantaneous velocity and speed of the ball at the end of3 seconds.Math 100 (Inst. of Mathematics)Derivatives19 / 27

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Examplesb)How many seconds does it take the ball to reach its highest point?How high will it go?

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Examples