Question

After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by the equation h = -16t² + 64t + 3. Determine how long it will take for the ball to hit the ground. Round your answer to the nearest hundredth... Please help .. It is due tomorrow

Answer 1

The ball will take 4.05 seconds to hit the ground.

Explanation:

we have

`h=-16t^(2)+64t+3`

This is a quadratic equation (vertical parabola) open down

The vertex is a maximum

we know that

The ball hit the ground when h=0

Solve the quadratic equation

For h=0

`-16t^(2)+64t+3=0`

The formula to solve a quadratic equation of the form

`at^(2) +bt+c=0` is equal to

`t=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`-16t^(2)+64t+3=0`

so

`a=-16\\b=64\\c=3`

substitute in the formula

`t=\frac{-64(+/-)\sqrt{64^(2)-4(-16)(3)}} {2(-16)}`

`t=\frac{-64(+/-)√(4,288)} {-32}`

`t=\frac{64(-)√(4,288)} {32}=-0.05\ sec` ---> the time cannot be a negative number

`t=\frac{64(+)√(4,288)} {32}=4.05\ sec`

therefore

The ball will take 4.05 seconds to hit the ground.