To find h(3), plug in t = 3 into the function:
h(3) = -16(3)^2 + 80(3) + 30
h(3) = -16(9) + 240 + 30
h(3) = -144 + 240 + 30
h(3) = 126 inches
Therefore, h(3) represents the height of the rock 3 seconds after it has been thrown, which is 126 inches.
To find h(2), plug in t = 2 into the function:
h(2) = -16(2)^2 + 80(2) + 30
h(2) = -16(4) + 160 + 30
h(2) = -64 + 160 + 30
h(2) = 126 inches
Therefore, h(2) also represents the height of the rock, which is 126 inches.
It does not make sense to find h(-1) in this context, as time cannot be negative in this scenario (a rock cannot be thrown before it is actually thrown).
A reasonable domain for this problem would be t ≥ 0, as time cannot be negative in this scenario.
a rock is thrown from one side of a river to another. The function h (t) = -16t^2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.
Find h (3). \
What does h(2) represent in the context of this problem?
Does it make sense to find h (-1) in the context of this problem?
What is a reasonable domain given the context of this problem?
3 answers
a better domain would be 0 ≤ t ≤ 5.35, since the rock hits the ground at t=5.35
You are correct. A better domain for this problem would be 0 ≤ t ≤ 5.35, since the rock hits the ground at t = 5.35 seconds. Thank you for pointing that out.