Question

The function f(t)=16t2 represents the distance (in feet) a dropped object falls in t seconds. The function g(t)=s0 represents the initial height (in feet) of the object. A coin purse is dropped from a height of 144 feet. After how many seconds does the coin purse hit the ground?

Answer 1

Answer:

After 3 sec the object touches the ground

Step-by-step explanation:

The initial height of the object is $s_0 = 144\ feet$

The function that represents the distance of the object as a function of time is:

$f (t) = 144-16t ^ 2$

So, when the object touches the ground we have to:

$f (t) = 0$

So:

$0 = 144 - 16t ^ 2$

$16t ^ 2 = 144$

$f (t) = g (t)$

We solve the equation for t:

$t ^ 2 = \frac{144}{16}$

$t ^ 2 = 9$

$t = +3$    and     $t = -3$

We take the positive solution.

$t = 3\ sec$.

After 3 sec the object touches the ground