# calculus 2

posted by .

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 -

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

## Similar Questions

1. ### MATH

The height h in feet of an object after t seconds is given by the function h=-16t^2+60t+9.... How long will it take the object to hit the ground?
2. ### Physics

An object is allowed to fall freely near the surface of an unknown planet. The object falls 80 meters from rest in 5.0 seconds. The acceleration due to gravity on that planet is?
3. ### physics

acceleration due to gravity questions when an object is dropped from a height of 10m above the surface of the planet z, it takes 1.2 seconds for the object to reach the surface. what is the acceleration of a falling object near the …
4. ### Physics

From the top of a tower is an object with mass 25 kg which is lowered with ropes at a constant speed, 4 m / s to the ground. After 10 seconds the rope by which an object falls freely. From the moment there are 12 seconds to those standing …
5. ### Science

My mother in law falls from a 200m cliff. Answer the following. a. What is her acceleration after 2 seconds?
6. ### precalculus

The acceleration acting on a falling object due to gravity varies inversely with the square of the object's distance from the center of Earth. At the surface of Earth, where x = 1 Earth radius, the acceleration is y = 9.8 m/s2 1. Use …
7. ### Applied Calculus

Suppose that an object is thrown down towards the ground from the top of the 1100-ft tall Sears Tower with an initial velocity of – 20 feet per second (the negative velocity indicates that the object is moving towards the ground). …
8. ### Calc B/C

Assume no air friction and that the acceleration due to gravity is 10 meters/sec^2. A ball is moving horizontally at a rate of 5 meters/sec. until it falls off the edge of a platform. The height, h, of the platform would have to be …
9. ### Calculus

Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground. By measuring the impact, you determine that this terminal velocity is -49 m/sec. A. Write the equation representing …
10. ### Math

An object is thrown upward from the top of a 160-foot building with an initial velocity of 144 feet per second. The height, h, of the object after t seconds is given by the equation h=-16t^2+144t+160. When will the object hit the ground?

More Similar Questions