Posted by Rachel on Thursday, January 31, 2013 at 1:13am.
An object falls off a 400-foot tower. With g=32ft/sec^2, as at the Earth’s surface, the object would hit the ground after 5 seconds. What would the acceleration due to gravity have to be to make it reach the ground in half the time?
- calculus 2 - Reiny, Thursday, January 31, 2013 at 8:46am
should have been g = -32
v = -32t + c, but when t = 0 , v = 0 , so c = 0
we have v(t) =-32t
a(t) = -16t^2 + k, when t = 0 , s = 400 , so k = 400
so our distance equation is
s(t) = -16t^2 + 400
when it hits the ground, s = 0
0 = -16t^2 + 400
t^2 = 25
t = 5
which was given, and is correct
if we didn't know the acceleration, let it be a
our distance equation would have been
s(t) = (a/2)t^2 + 400
at half the time, t = 2.5
0 = (a/2)(6.25) + 400
a/2 = -400/6.25
a = -800/6.25 = -128 ft/sec^2
Answer This Question
More Related Questions
- Physics - From the top of a tower is an object with mass 25 kg which is lowered ...
- Physics - An object is allowed to fall freely near the surface of an unknown ...
- Applied Calculus - Suppose that an object is thrown down towards the ground from...
- MATH - The height h in feet of an object after t seconds is given by the ...
- Calc B/C - Assume no air friction and that the acceleration due to gravity is 10...
- Science - My mother in law falls from a 200m cliff. Answer the following. a. ...
- precalculus - The acceleration acting on a falling object due to gravity varies ...
- Check Math - Old Isaac took a little nosedive from his perch on Mrs. Cohen’s ...
- Physics - From the top of a tower is an object with mass 25 kg is lowered at ...
- physics - acceleration due to gravity questions when an object is dropped from a...