Calculus: Limit Word Problems

label Calculus
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Use the position function s(t) = -16t^2+1000, which gives the height (ft) of an object that has fallen for t seconds from a height of 1000 ft. The velocity at time t=a seconds is given by

lim    s(a) - s(t)
t->a     a-t        .

101. If a construction worker drops a wrench from a height of 1000 ft, how fast will the wrench be falling after 5 seconds?

102. If a construction worker drops a wrench from 1000 ft, when will the wrench hit the ground? At what velocity will the wrench impact the ground?

Sep 1st, 2015

101. If a construction worker drops a wrench from a height of 1000 ft, how fast will the wrench be falling after 5 seconds?

VELOCITY = (S(a-s(t))/a-t

s(t)

t=0

s(t) =100

s(a)

a =5

s(a)=-16(5^2)+1000=  600

velocity = 600-1000/5-0 =  -80m/s ( negative indicates direction)  = 80m/s

Sep 1st, 2015

How would you do question 102?

Sep 1st, 2015

101. If a construction worker drops a wrench from a height of 1000 ft, how fast will the wrench be falling after 5 seconds?

VELOCITY = (S(a-s(t))/a-t

s(t)

t=0

s(t) =1000

s(a)

a =5

s(a)=-16(5^2)+1000=  600

velocity = 600-1000/5-0 =  -80ft/s ( negative indicates direction)  = 80ft/s

102. If a construction worker drops a wrench from 1000 ft, when will the wrench hit the ground? At what velocity will the wrench impact the ground?

At ground S(a) = 0

0 =  -16t^2+1000

16t^2 = 1000

t^2= 1000/16

t =square root of 62.5

t=7.906 sec

Rench hits ground after 7.906 sec

velocity

s(a) =0

s(t) = 1000

velocity = 0-1000/7.906 = 126.5ft/s

Sep 1st, 2015

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Sep 1st, 2015
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Sep 1st, 2015
Aug 18th, 2017
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