Question

Help asap will give briniest.

Answer 1

3 seconds.

Explanation:

1. Identify the given values.

The problem states that the ball was kicked from a height of 12 ft, this would be the initial height of the ball. Hence:

h₀= 12 ft

Also, initial velocity is 44ft/s. Hence:

v₀= 44ft/s

2. Substitute the variables by the given values in the formula.

`h(x)=-16x^(2) +v_(0) x+h_(0) \\ \\h(x)=-16x^(2) +(44ft/s) x+(12ft)`

3. Rewrite as a common mathematical equation.

`h(x)=-16x^(2) +44 x+12`

4. Solve for time (x).

Since the height when the ball hits the ground is 0, we need to substitute the height value (h(x)) by 0, and then solve the equation for "x".

Using the quadratic formula (check the attached image) we can get the value of time.

Taking the coefficients:

A= -16

B= 44

C= 12

`x_(1) =\frac{-(44)+\sqrt{(44)^(2)-4(-16)(12) } }{2(-16)}= -0.25s\\ \\x_(2) =\frac{-(44)-\sqrt{(44)^(2)-4(-16)(12) } }{2(-16)} =3s`

Since "x" is being used to represent time, and time is a variable that can only be positive, we're only taking the positive value.

Hence, we can conclude that after 3 seconds after being kicked, the ball wil hit the ground.