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).