We are given an equation that models the height of a ball.
h(t)=- 16t^2+40t+5
To find when the ball hits the ground, we need to find the time when the height is 0. We can do this by solving a quadratic equation.
- 16t^2+40t+5=0Let's use the Quadratic Formula.
lc
Quadratic equation:& ax^2+ bx+ c=0 [0.5em]
Solutions:&x=- b±sqrt(b^2-4 a c)/2 a
Let's identify the coefficients in our quadratic expression.
- 16t^2+ 40t+ 5
We see that a= - 16, b= 40, and c= 5. Substitute these values into the Quadratic Formula.
Let's use a calculator to find approximate values of these solutions.
-40+sqrt(1920)/-32≈ -0.12 [0.5em]
-40-sqrt(1920)/-32≈ 2.62
Since the solution we are looking for represents time, we need the positive solution. The ball will hit the ground 2.62 seconds after Lauren threw it.
