Question

The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it.

What is the value of ​v0​?

Answer 1

v0 = 32 ft/s

Explanation:

Answer 2

`\large \boxed{\sf \ \ v_0=32 \ \ }`

Explanation:

Hello,

The equation is

`y=f(x)=-16x^2+v_0 \cdot x`

The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.

We need to find
`v_0` such that f(2)=0.

`f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=(64)/(2)=32`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you