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.

Question

11-11-2016
Physics

Answered

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.

Answer :

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t | 2 3 4 5
H(t)| 208 224 208 160
g(t) | 95.4 127.6 159.8 192

A) The solution lies between 4 and 5 seconds. This is because H(t) is decreasing with time and g(t) is increasing. The values of both approach one another between 4 and 5 seconds and become the closest, but then start to diverge again.

B) The solution of the equation system will give the time at which the two objects are at the same height.