Question

The function H(t)=-16t+48t+12 shows the height H(t), in feet, of a cannon ball afte t seconds. A second cannon ball moves in the air along a path represented by g(t)=10+15.2t, 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 0 through 3 for the 2 functions. Between wat 2 seconds is the solution to H(t)=g(t) located? How do you know?
Part B: Explain what the solution from Part A means in the context of the problem.

Answer 1

Part A:

The table is shown in the first picture below

From the tables, we can read that the solution
`H(t)=G(t)` is located between 0 and 2 seconds.

The reason is that in between the interval of 0 and 2,
`H(t)` is turning (the cannon ball is moving toward the ground) whereas the function
`G(t)` increase its height. At one point these two paths will cross, as shown in the graph in the second picture below

Part B:

In the context of the problem, the one point where
`H(t)` and
`G(t)` crosses is the point where the two cannon balls will collide.