Use the function h(t)=-16t2+vot+s to answer the question.

Question

An object is launched upward from the ground at an initial speed of 112 feet per second. How long will it take until the object lands on the ground?

Answer 1

In the given formula v₀ is 112 ft/sec (initial velocity). Since the object is thrown from ground level the initial height is 0 (s).

h(t) = -16t²+112t

When the object finally returns to earth its height will be zero, so we want to know when h(t) = 0.

-16t²+112t = 0

A quadratic equation that can be solved by factoring:

-4t(4t - 28) = 0

-4t = 0 or 4t-28 = 0

t = 0 (not the time we are looking for, this is the initial time when the object was at ground level)

4t=28

t = 7

The object hits the ground after 7 seconds.

Here is a graph depicting the vertical motion of the object. If you take a look you will see that the graph is a parabola. If instead the question has asked what is the max height of the object. the coordinates of the vertex would answer that question.

desmos.com/calculator/lsvmbftasx