Calculus: Limit Word Problems

Calculus
Tutor: None Selected Time limit: 1 Day

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

Thank you for the opportunity to help you with your question!

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


Please let me know if you need any clarification. I'm always happy to answer your questions.
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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Sep 1st, 2015
...
Sep 1st, 2015
May 23rd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer