Assuming you mean y = 200 - 16t^2, we have all the required information needed to solve this problem. The y-value is the height of the building and the t-value represents the number of seconds after the shoe fell off.
Since we are trying to solve <em>for t</em>, we will be using our y-value. The problem states that we landed on a building with a height of 31 feet. We can plug this into the y-value, since that is what y is defined as (the height of the building).
Now we have:
31 = 200 - 16t^2
We can solve this to find t:
-169 = -16t^2
169 = 16t^2
10.5625 = t^2
3.25, -3.25 = t
We have found two answers for t. However, the negative value is not a solution because we can not have a negative number of seconds. Thus, 3.25 is the only value of t which works for this problem.
Since t is the value we are trying to find, we have our answer. The shoe hits the building after 3.25 seconds.
We cannot answer since we do not have the picture or diagram.
