Question

The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 20 + 38.7t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points) (10 points)

Answer 1

We are given the functions:

h(t) = -16t^2 + 60t + 95

g(t) = 20 + 38.7t

Part A. All we have to do is to plug in the value of t = 1 to 4 on the two functions

t               h(t)          g(t)

1              139         58.7

2              151         97.4

3              131         136.1

4              79           174.8

Looking at the table, we can say that the time when h(t)=g(t) must be between t=2 and t= 3 seconds
At t=2 seconds h(t) is above g(t), and at t = 3 seconds h(t) is below g(t). Therefore the two functions must be at the same height in between.

 

Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that h(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.