Question

Pls help

The function H(t) = −16t2 + 75t + 25 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 5 + 5.2t, 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?

Part B: Explain what the solution from Part A means in the context of the problem.

Answer 1

check the first picture below.

those are the table of values we get for both, at 1 through 5 seconds.

why are both functions equal between the 4th and 5th second?

h(t) is the distance from the ground, check the second picture below, that's pretty much the graph of h(t) usually.

g(t) is the height of the object from the ground.

whilst g(t) is ever increasing, h(t) goes up, reaches a peak point, the vertex, and then goes back down, on its way down, it drops to 69 and then to 0 at the 5th second, however, between 69 and 0, it dropped first to 31 at some time, and then 30, then 29, then 27, then 25.8 and so on till it got to 0.

one of those values between 69 and 0, will match a value between 25.8 and 31.

what does all that mean in this context?

it means that at some point the baseball was at a height predicted g(t) as well as by h(t).