Question

The function H(t) = −16t2 + 80t + 112 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 20 + 5.2t, 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 3 through 6 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)

Answer 1

The table for
`H(t) = -16t^2 + 80t + 112` is given below:
t t^2 -16t^2 80t +112 H(t)
3 9 -144 240 112 208
4 16 -256 320 112 176
5 25 -400 400 112 112
6 36 -576 480 112 16

The table for
`g(t) = 20 + 5.2t` is given below:
t 20 5.2t g(t)
3 20 15.6 35.6
4 20 20.8 40.8
5 20 26 46
6 20 31.2 51.2

From the table, the solution to H(t) = g(t) is located between 5 seconds and 6 seconds.

b.) the solution in part A means that at a time between5 and 6 seconds the height of the ball represented by H(t) is equal to the height of the ball represented by g(t).