Help Please?

Question

If a pebble is dropped toward a pond from the top of a 360-ft building, its height, h, after t seconds is given by h = -16t ^2+180. How long does it take the pebble to pass through a height of 60 feet?

Answer 1

Doug is right. The given equation h=-16t^2+180 suggest that the the stone has a maximum height of 180ft, unless height is measured not in feet but half-feet or unless the pond is somehow 180 ft from the top of the building (180ft of the building is beneath the water level?) Also, the wording "to pass through a height of 60 feet" is subject to question as well. I would like to interpret this as how long does it take to pass through the point of height 60 ft which would be an infinitely small amount of time.

But we'll do this:
Assuming the pond is at the base of the 360 ft building we will consider h ranging from 180 ft (top of building) to -180 ft (pond). We will consider three interpretations of the question!
1)...After falling 60 ft: h= 120ft t= 1.94s
2)... h= 60ft t= 2.74s
3)...After falling 300ft to a height of 60ft: h= -120ft t=3.54s
4)...Falling from a height of 60 ft to a height of 0 ft: h starts at -120ft (t= 4.33s) and ends at -180ft (t= 4.74) though which 0.413 seconds occur.
Each could be argued as the correct answer to your question, as well as a few other broader interpretations. I REALLY hope this helps.

Answer 2

Errrmmmmm...... Don't look now, but that equation is wrong . It should be h = -16t² + 360
So how long does it take to get to 60 feet? Solve for t
t = √((360-h)/16) and plug in 60 for h to get
t = √((360 - 60)/16) = √(300/16) = √(18.75) = 4.33 s.

See how easy it is when you use the formulas with a bit of algebra? ☺


Doug

Answer 3

Substitute it:

h=60 ft

60=-16t^2 + 180
16t^2=120
t=sqrt of 120/16
t=2.738612788

Answer 4

h = -16t ^2+180
when h=60 then
60 = -16t^2 +180
16t^2=120
t^2 = 120/16=7.5
t =sqrt 7.5 seconds=2.738612788 seconds