13) Suppose a construction worker drops a bolt from a scaffold high above a work

Question

13) Suppose a construction worker drops a bolt from a scaffold high above a work site. The distance it falls in t seconds is given by s()-81 64, where s(t) is in feet. Assuming that air resistance is negligible, find: (don't forget to use correct notation and label your units!) a) how far the bolt falls in 2 seconds. b) how fast the bolt is traveling 2 seconds after being dropped. c) the bolt's acceleration after it has been falling for 2 seconds. d) how far the bolt has traveled when its velocity measures 112 feet/sec.

Explanation / Answer

s = 8t^2 + 64t

a) in 2 secs :
s = 8(2)^2 + 64(2)
s = 8(4) + 128
s = 160

So, it falls 160 ft in 2 seconds

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b)
s(t) = 8t^2 + 64t

Deriving, we get velocity :
v(t) = 16t + 64

Now, plug in t = 2 :
v(2) = 16(2) + 64
= 96 ft/sec

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c)
a(t) = derivative of v(t)

a(t) = 16

So, acc is 16 ft/sec^2

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d) First lets find the time when v = 112 ft/sec

112 = 16t + 64

t = 3

Now, find s(3)....
s = 8t^2 + 64t

s(3) = 8(3)^2 + 64(3)

= 264 ft

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