A bouncy ball is dropped from a height of $144$ $144$ feet. The function $h = - 16 x^{2} + 144$ $h=−16x^2+144$ gives the height, $h$ $h$ , of the ball after $x$ $x$ seconds. When does the ball hit the ground?

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A bouncy ball is dropped from a height of $144$ $144$ feet. The function $h = - 16 x^{2} + 144$ $h=−16x^2+144$ gives the height, $h$ $h$ , of the ball after $x$ $x$ seconds. When does the ball hit the ground?

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Answer 1 · 2018-02-24T02:45:37

The ball will hit the ground in $3$ $3$ secs.

Explanation:

$16 x^{2}$ $16x^2$ must equal $+ 144$ $+144$ so that $h = 0$ $h = 0$ .

In other words, when the ball hits the ground, the distance above the ground will be zero.

That occurs $3$ $3$ seconds after the ball was released.

$0 = - 16 x^{2} + 144$ $0=-16x^2 +144$

$16 x^{2} = 144$ $16x^2 =144$

Answer 2 · 2018-02-24T02:48:40

$3$ $3$ seconds

Explanation:

$h (x) = - 16 x^{2} + 144$ $h(x)=-16x^2+144$ => the ball hits the ground at h = 0:
$- 16 x^{2} + 144 = 0$ $-16x^2+144=0$
$- 16 (x^{2} - 9) = 0$ $-16(x^2-9)=0$
$x^{2} = 9$ $x^2=9$
$x = \pm 3$ $x=+-3$ => reject the negative time, thus:
$x = 3$ $x=3$ the ball hits the ground 3 seconds after it was dropped

Answer 3 · 2018-02-24T06:23:11

The ball hits the ground after $3$ $3$ seconds.

Explanation:

When the ball is dropped, the height will get less and less. When it hits the ground the height will be $0$ $0$

$0 = - 16 x^{2} + 144 \leftarrow$ $0 = -16x^2 +144" "larr$ now solve the equation,

You can isolate the $x$ $x$ term:

$0 = - x^{2} + 9 \leftarrow \div 16$ $0 = -x^2 +9" "larr div 16$

$x^{2} = 9$ $x^2 = 9$

$x = \pm \sqrt{9}$ $x =+-sqrt 9$

$x = + 3 or x = - 3$ $color(blue)(x = +3) or x=-3$

You could also factorise:

$0 = 144 - 16 x^{2} \leftarrow$ $0 =144-16x^2" "larr$ difference of two squares.

$0 = 9 - x^{2} \leftarrow \div 16$ $0 = 9-x^2" "larr div 16$

$0 = (3 + x) (3 - x)$ $0 = (3+x)(3-x)$

$x = - 3 or x = + 3$ $x= -3 or color(blue)(x=+3)$

In each case reject $- 3$ $-3$ because the time cannot be negative,

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A bouncy ball is dropped from a height of $144$ $144$ feet. The function $h = - 16 x^{2} + 144$ $h=−16x^2+144$ gives the height, $h$ $h$ , of the ball after $x$ $x$ seconds. When does the ball hit the ground?

3 Answers

Explanation:

Explanation:

Explanation:

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A bouncy ball is dropped from a height of 144144 feet. The function h=−16x2+144h=−16x^2+144 gives the height, hh, of the ball after xx seconds. When does the ball hit the ground?

3 Answers

Explanation:

Explanation:

Explanation:

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A bouncy ball is dropped from a height of $144$ $144$ feet. The function $h = - 16 x^{2} + 144$ $h=−16x^2+144$ gives the height, $h$ $h$ , of the ball after $x$ $x$ seconds. When does the ball hit the ground?