Calculus: Limit Word Problems
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 at .
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?
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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(as(t))/at
s(t)
t=0
s(t) =100
s(a)
a =5
s(a)=16(5^2)+1000= 600
velocity = 6001000/50 = 80m/s ( negative indicates direction) = 80m/s
How would you do question 102?
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(as(t))/at
s(t)
t=0
s(t) =1000
s(a)
a =5
s(a)=16(5^2)+1000= 600
velocity = 6001000/50 = 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 = 01000/7.906 = 126.5ft/s
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