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When an object is dropped on a certain earth-like planet; the distance it falls in t seconds, assuming that air resistance is negligible, is given by s(t) = 19t 2 where​ s(t) is in feet. Suppose that a​ medic's reflex hammer is dropped from a hovering helicopter. Find ​(a) how far the hammer falls in 3 ​sec, ​(b) how fast the hammer is traveling 3 sec after being​ dropped, and ​(c) the​ hammer's acceleration after it has been falling for 3 sec.

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Answer:

171 ft

114 ft/s

38 ft/s²

Explanation:

The function is [tex]s(t)=19t^2[/tex]

At s = 3 s

[tex]s(3)=19\times 3^2\\\Rightarrow s(3)=171\ ft[/tex]

The hammer falls 171 ft

Differentiating the function with respect to time we have

[tex]v=\dfrac{d}{dt}19t^2\\\Rightarrow v=38t[/tex]

at t = 3 s

[tex]v=38\times 3\\\Rightarrow v=114\ ft/s[/tex]

The velocity of the hammer is 114 ft/s

Differentiating with v respect to t

[tex]a=\dfrac{d}{dt}38t\\\Rightarrow a=38\ ft/s^2[/tex]

The acceleration is 38 ft/s²

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