Question

Jennifer hit a golf ball from the ground, and it followed the projectile h(t)=-16t^2+100, where t is the time in seconds, and h is the height of the ball

Answer 1

Answer:
`2.5\ seconds`

Explanation:

The complete exercise is: "Jennifer hit a golf ball from the ground and its movement follows the equation
`h(t)=-16t^2+100`, where t is the time in seconds, and h(t) is the height of the ball at a given time "t". Find the time that it took the golf ball to hit the ground."

The quadratic function is:

`h(t)=-16t^2+100`

Since the ground is at
`h(t)=0`, you need to substitute this into the function:

`0=-16t^2+100`

Now you must solve for "t". The steps are:

- You need to subtract 100 from both sides:

`0-100=-16t^2+100-100\\\\-100=-16t^2`

- Now you must divide both sides of the equation by -16:

`(-100)/(-16)=(-16t^2)/(-16)\\\\6.25=t^2`

- Applying the square root both sides of the equation, you get:

`\±√(6.25) =√(t^2)\\\\t_1=2.5\\\\t_2=-2.5`