Answer:
- Part A:<u> Between t = 3 seconds and t = 4 seconds.</u>
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- Part B: <u>the solution is the moment when the two baseballs have the same height.</u>
Explanation:
The functions are garbled. The correct functions are:
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?
Table:
t(s) H(t) = -16t² + 64t + 12 g(t) = 10 + 1.4t
1 -16(1)² + 64(1) + 12 = 60 10 + 1.4(1) = 11.4
2 -16(2)² + 64(2) + 12 = 76 10 + 1.4(2) = 12.8
3 -16(3)² + 64(3) + 12 = 60 10 + 1.4(3) = 14.2
4 -16(4)² + 64(4) + 12 = 12 10 + 1.4(4) = 15.6
The solution is between t = 3 s and t = 4 s.
You know it because the two functions are continuous, and at t = 3 seconds H(t) is greater than g(t), while at t = 4 seconds H(t) is greater than g(t). Thus, necessarily at one instant between t = 3 seconds and t = 4 seconds the two functions have the same value.
Part B: Explain what the solution from Part A means in the context of the problem.
The solution is the point of intersection of the graphs. Since each graph is the path of a ball, the point of intersection is when the two paths intersect.
Then the solutions means that the two baseballs are at the same height at a time between t = 3 seconds and t = 4 seconds.
You cannot assure that the two balls collide with each other because the function only shows height, but not the other coordinates in the space.