# Math Help - Falling object problem. ..

1. ## Falling object problem. ..

suppose an object is dropped from a height of x above the ground. Then its height after t seconds is given by h=-16t²+x, where h is measured in feet. Use this info to solve the problem.

A ball is dropped from the top of a building 96 ft tall.

How long will it take to fall half the distance to ground level??

How do you solve this? Thanks.

2. Originally Posted by Godzilla
suppose an object is dropped from a height of x above the ground. Then its height after t seconds is given by h=-16t²+x, where h is measured in feet. Use this info to solve the problem.

A ball is dropped from the top of a building 96 ft tall.

How long will it take to fall half the distance to ground level??

How do you solve this? Thanks.
Well, you are given that x=96feet.

so put that in

$h=-16t^2+96$

and this gives the height after t seconds.

now you want to find t when the thing is half its initial hieght, so

$\frac{1}{2}96=h=-16t^2+96$

solve for t

I just edited my post, I copied and pasted alot from yours and assumed tha it would remain the same (the t did not stay squared). Sorry if there was any confusion.

3. $h = -16t^2 + x$

At time , t = 0 h = 96 ft $96 = - 16(0)^2 + x$

therefore , x = 96

we get this equation $h = -16t^2 + 96$

$h = 0.5(96) = 48$ sub into the equation

$48 = -16t^2 + 96$

$-48 = -16t^2$

$t ^ 2 = 3$

$t = \sqrt{3}$