Homework Help: calculus 2

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
then
v = -32t + c, but when t = 0 , v = 0 , so c = 0

we have v(t) =-32t
then
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
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

Related Questions

Physics - From the top of a tower is an object with mass 25 kg which is lowered ...
physics - when an object is 100m above the surface of earth. The earth's ...
math - the distance, d, an object falls when dropped from a tower varies ...
Physics - Suppose a new extrasolar planet is discovered. Its mass is double the ...
Physics - How far above the surface of the Earth does an object have to be in ...
physics - The earth has a radius of 6380 km and turns around once on its axis in...
Check Math - Old Isaac took a little nosedive from his perch on Mrs. Cohen’...
calculus - an object is dropped from a tower. the distance in t seconds is given...
Algebra II - The force of attraction between the earth and some object is called...
physics - A popular pastime is to see who can push an object closest to the edge...

For Further Reading

First Name:
School Subject:
Answer: