Question

The formula to show the height and time an object is in the air is given byh(t) = -16t2 + 48t + 50 where h(t) is the height of an object and t is the timein seconds. Find how long the object is in the air before it hits the ground.

Answer 1

The formula to show the height and time an object is in the air :

`h(t)=-16t^2+48t+50`

when the object hits the ground the height will become 0

so, put h(t) = 0

and simplify :

`\begin{gathered} h(t)=-16t^2+48t+50 \\ 0=-16t^2+48t+50 \\ -16t^2+48t+50=0 \end{gathered}`

Simplfy the equation by using discrimination rule :

The general form of quadratic equation is : ax² + bx + c

and the roots are express a s :

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

On compare the given equation with the general equation we get :

a = -16, b = 48 and c = 50

Substitute the value and simplify :