Ted throws an object straight up into the air with an initial velocity of 54 ft/s from a platform that is 40 ft above the ground. Use the formula h(t)=−16t2+v0t+h0, where v0 is the initial velocity and h0 is the initial height. How long will it take for the object to hit the ground?

The time it will take for the object to hit the ground will be 4.

Explanation:

You have:

h(t)=−16t²+v0*t+h0

Being v0 the initial velocity (54 ft/s) and  h0 the initial height (40 ft) and replacing you get:

h(t)=−16t²+54*t+40

To know how long it will take for the object to touch the ground, the height h(t) must be zero. So:

0=−16t²+54*t+40

Being a quadratic function or parabola: f (x) = a*x² + b*x + c, the roots or zeros of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the points where the parabola intersects the x axis. To calculate the roots the expression is used:

In this case you have that:

Replacing in the expression of the calculation of roots you get:

 Expresion (A)

and

Expresion (B)

Solving the Expresion (A):

Solving the Expresion (B):

These results indicate the time it will take for the object to hit the ground can be -5/8 and 4. Since the time cannot be negative, then the time it will take for the object to hit the ground will be 4.

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