A ball is thrown from a height of

105
feet with an initial downward velocity of
9/fts
. The ball's height
h
(in feet) after
t
seconds is given by the following.
=h−105−9t16t2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

You mean

g = - 32 ft/s^2
so
h = Hi + Vi t + (1/2)a t^2

h = 105 - 9 t - 16 t^2
at ground:
0 = 105 - 9 t - 16 t^2
or
16 t^2 + 9 t - 105 = 0

t = [ -9 +/- sqrt(81+6720)]/32

t = [-9 +/- 82.5 ]/32
use positive time
2.30 seconds

h(t) = 105 - 9t - 16t^2

When does it hit the ground? That would be when h(t) = 0, right?

So, just solve the quadratic equation.

Well, it sounds like this ball is really throwing itself into the ground. It must be really clumsy or something. Anyway, to find out how long it takes for the ball to hit the ground, we need to set the height equal to zero. So, let's set h - 105 - 9t + 16t^2 equal to zero. Now, we just need to solve this quadratic equation and find the value(s) of t when the height is zero. Good luck!

To find out how long it takes for the ball to hit the ground, we need to find the value of t when the height (h) is equal to zero. So we'll set the equation equal to zero and solve for t.

The equation representing the ball's height is:

h = -105 - (9/16)t + 9t^2

Setting h to zero:

0 = -105 - (9/16)t + 9t^2

Now, we can solve this quadratic equation. Let's multiply the whole equation by 16 to remove the fraction:

0 = -1680 - 9t + 144t^2

Rearranging the equation:

144t^2 - 9t - 1680 = 0

This is a quadratic equation in standard form. We can solve it using factoring, completing the square, or the quadratic formula.

In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

where a = 144, b = -9, and c = -1680.

Plugging in the values:

t = (-(-9) ± √((-9)^2 - 4(144)(-1680))) / (2(144))

t = (9 ± √(81 + 967680)) / 288

t = (9 ± √967761) / 288

Now we can calculate the two possible values for t:

t1 = (9 + √967761) / 288
t2 = (9 - √967761) / 288

Rounding the answers to the nearest hundredth:

t1 ≈ 5.14 or t2 ≈ -1.19

Since time cannot be negative, the ball hits the ground approximately 5.14 seconds after it is thrown.

2.67