Question

The function H(t) = −16t^2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, 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 4 through 7 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

Answer:

see the attachment for a table

Step-by-step explanation:

A. The table is shown in the attachment. The solution to h(t) = g(t) is at a value of t that lies between 6 and 7. At t=6, h(t) > g(t). At t=7, h(t) < g(t). Since both functions are continuous, they must have equal values somewhere between t=6 and t=7. (Intermediate value theorem.)

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B. The solution means the cannon balls will have the same height at a value of t between 6 and 7.