Question

The function H(t) = −16t2 + 90t + 50 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) = 28 + 48.8t, 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)

Answer 1

For the answer to the question above,
For the answer to Part A
      
         H(t)       g(t)
1     124      76.8
2     166      125.6
3     176      174.4
4     154      223.2

The solution is between 3 and 4 seconds because it can be seen that there was a shift in the trend between them. H(t) had higher values for the first 3 seconds. It can be seen that in 3 seconds, g(t) is already approaching H(t). Finally, at 4 seconds, g(t) surpasses H(t).

For the answer to part B
This means that between 3 and 4 seconds, g(t) was able to catch up to H(t) in terms of height. At H(t)=g(t), this gives 3.03 secs which is indeed between 3 and 4 seconds. Above 3.03 seconds, g(t) overtakes the height of H(t).