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

Answer 2

Answer:

The coin purse hit the ground in 3 seconds.

Step-by-step explanation:

Given :

$\rm f(t) = 16 t^2$   ----- (represent the distance(in feet) a dropped object falls in t seconds)

$\rm g(t) = s_0 = 144ft$  ------ (represent the initial height (in feet) of the coin purse)

Calculation:

The function that represents the distance a dropped coin purse falls in t seconds,

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

When the coin purse touches the ground,

$\rm f(t) = 0$

$\rm 0 = 144-16t^2$

$\rm t^2 = \dfrac {144}{16} = 9$

t = +3 and t = -3

So we take positive t.

Therefore, the coin purse hit the ground in 3 seconds.

For more information, refer the linbk given below

https://brainly.com/question/12431044?referrer=searchResults