The function H(t) = −16t^2 + 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.

Question

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)

*** I think it is bewteen 3 and 4 because those are the two closest***

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

***they will meet after between 3 or 4***

Answer 1

You want to find:

−16t^2 + 90t + 50 = 28 + 48.8t
16t^2 -41.2t - 22 = 0
by the formula:
t = (41.2 ± √3105.44)/32
= appr 3.03 or -.454

so you are correct, it is between 3 and 4, much closer to 3 seconds