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Use the position function s(t) = –16t2 + 800, which gives the height (in feet) of an object that has fallen for t seconds from a height of 800 feet. The velocity at time t = a seconds is given by the following.If a construction worker drops a wrench from a height of 800 feet, how fast will the wrench be falling after 3 seconds?

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MechEngineer

Answer:

96 ft/s

Step-by-step explanation:

We can start by deriving the equation of the velocity, which is the derivative of the position equation:

[tex]v(t) = \frac{ds}{dt} = (-16t^2)' + 800' = -32t[/tex]

After 3 seconds, the wrench would achieve a speed of

v(3) = -32t = -32*3 = -96 ft/s

So it's falling at the rate of 96 ft per second after 3 s

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