Question

The function H(t) = −16t2 + 96t + 80 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) = 31 + 32.2t, 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 2 through 5 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

Given that the projectiles have been given by the functions:
H(t)=-16t^2+96t+80 and G(t)=31+32.2t
Part A:
The tables for the functions will be as follows:
t 2 3 4 5
H(t) 208 224 208 160

t 2 3 4 5
G(t) 95.4 127.6 159.8 198

The solution is found between points:
4th second and 5th second

i] It's between this point that the graph H(t) is has reached the maximum point and it's now turning. So the points of H(t) are nearing points for G(t).

Part B]
The solution in part A implicates the times at which the projectiles were at the same height and the time at which they were at the same heights.