The height of an object launched vertically upward is given by the function h(t)=200+11t-4.9t^2, where h is in meters and t is in seconds. What is the object’s approximate speed when it hits the ground?

The approximate speed of the object when it hits the ground is 63.568 meters per second.

Explanation:

The height of the object launched vertically upward is represented by the function . The approximate speed of the object when it hits the ground occurs when . Then, we solve the resulting second-order polynomial by the Quadratic Formula:

(1)

The roots associated to this polynomial are, respectively:

and

Given that time is a positive variable, the only solution that is physically reasonable is:

The function velocity is the first derivative of the function defined at the commencement of the explanation, that is:

(2)

If we know that , then the approximate velocity of the object when it hits the ground is:

The speed is the magnitude of this velocity. Therefore, the approximate speed of the object when it hits the ground is 63.568 meters per second.