Question

A coin is dropped from a height of 750 feet, the height (in feet),at time(in seconds) is giving by:
f(x)=-16t^2+750
Find the average velocity starting at 3 seconds and lasting:
a. 0.5 seconds
b. 0.1seconds

and find the instantaneous velocity at 3 seconds?

Answer 1

hi

Answer 2

hi

Answer 3

what expression does your book use for avg velocity?

Answer 4

i can't find it

Answer 5

darn

Answer 6

A)104 ft/sec

Answer 7

can you give me the formula ?

Answer 8

Do you have your 5 equations that go with free fall and gravity?

Answer 9

\[\frac{ f(x)-f(y) }{x-y }= V _{av}\] where x and y are time variables and x>y.

Answer 10

to find the instantaneous velocity just derivate the above expression and insert 3 in place of x.

Answer 11

?

Answer 12

He means take the derivative of -16t^2+750...then plug in 3 for t and solve to get the instantaneous velocity at 3 seconds.

Answer 13

I dont think he uses derivatives... He probably is doing mechanics ( thats how we call it here). Do you have the formular such has Vf = at^2+ 1/2(a)(t) or something. Its not very clear in my memory but this is one of the 5 equation your teacher should have given you if you haven't taken calculus 1 yet :)

Answer 14

\[V(t) = V _{0} + at\]

Answer 15

http://mahdisjalalvandi-sph3u.blogspot.ca/2010/10/big-5-kinematic-equations.html there are your formulas ( I took that about 2 years ago and personally dont use them anymore, I just go with what Im given). Hope it helps :)

Answer 16

The equation for the height at time t is:
\[h=-16t^2+750\]Part a:\[h_i=-16(3s)^2+750=606ft\]\[h_f=-16(3.5s)^2+750=554ft\]\[\Delta h = h_f-h_i=554ft-606ft=-52ft\]\[V_{avg}=\frac{\Delta h}{\Delta t}=\frac{-52ft}{0.5s}=-104ft/s\]
Part b:
\[h_i=-16(3s)^2+750=606ft\]\[h_f=-16(3.1s)^2+750=596.24ft\]\[\Delta h = h_f-h_i=596.24ft-606ft=-9.76ft\]\[V_{avg}=\frac{\Delta h}{\Delta t}=\frac{-9.76ft}{0.1s}=-97.6ft/s\]
Part c:
Take the derivative of -16t^2+750:\[\frac{d}{dt}y'(-16t^2+750)=-32t\]Plug in 3 for t to get:\[(-32)(3s)=-96m/s\]

Answer 17

Oops...that last one should have been ft/s....not m/s. I'm used to metric units :)