Question

PLEASEE HELP!!

How long would it take a ball to reach the ground if the height was modeled by
h(t) = -4t2 + 12t + 100, where t is the time in seconds?
A) about 6.7 seconds
B) about 7.6 seconds
C) about 3.7 seconds
D) about 5.2 seconds

Answer 1

A)t=6.7

Explanation:

to understand this

you need to know about:

• quadratic equation
• quadratic equation word problems
• solving quadratic

given:

h(t) = -4t² + 12t + 100

to solve:

t

tips and formulas:

• the Ball will hit the ground when the height is 0
• solving quadratics using quadratic formula
• PEMDAS

let's solve:

`- 4 {t}^(2) + 12t + 100 = 0`

`step - 2 : \\ divide \: both \: sides \: by \: - 4`

`{t}^(2) - 3t - 25 = 0`

`step - 3 : \\ solve \: the \: quadratic`

`formula : \\ x = \frac{ - b± \sqrt{ {b}^(2) - 4ac } }{2a}`

`t = \frac{ - ( - 3)± \sqrt{ {( - 3)}^(2) - 4.1. - 25 } }{2.1}`

`t = ( 3± √( 9 + 100) )/(2)`

`t = (3 + √( 109 ) )/(2)`

`t = (3 - √( 109 ) )/(2)`

`t = 6.7 \\ t = - 3.7`

`as \: we \: know \: time \: cannot \: be \: negative`

`\huge \therefore \: t = 6.7`