MATH SOLVE

2 months ago

Q:
# Item 20 You are riding a roller coaster when a shoe falls off your foot. The function y=200−16t2 represents the height y (in feet) of the shoe t seconds after it falls off your foot. The shoe lands on the top of a 31-foot-tall building. After how many seconds does the shoe hit the building?

Accepted Solution

A:

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 for t, 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.

Since we are trying to solve for t, 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.