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

Given:
h(t) = -16t² + 90t + 50
g(t) = 28 + 48.8t

h(1) = -16(1²) + 90(1) + 50 = 124
h(2) = -16(2²) + 90(2) + 50 = -64 + 180 + 50 = 166
h(3) = -16(3²) + 90(3) + 50 = -144 + 270 + 50 = 176
h(4) = -16(4²) + 90(4) + 50 = -256 + 360 + 50 = 154

g(1) = 28 + 48.8(1) = 76.80
g(2) = 28 + 48.8(2) = 125.60
g(3) = 28 + 48.8(3) = 174.40
g(4) = 28 + 48.8(4) = 223.20

Between 3 seconds is the answer... though it is not exactly equal but they are nearer in value compared to other number of seconds.