The equation h = -16t ^2 + 112t gives the height of a narrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.
2007-10-20 08:52:01 · 2 answers · asked by Mommy-fied 5 in Science & Mathematics ➔ Mathematics
Replace h with 180.
180 = -16t^2 + 112t
16t^2 - 112t + 180 = 0.
Divide the equation by 4.
4t^2 - 28t + 45 = 0
Factor:
(2t - 9)(2t - 5) = 0
t = 4.5 or t = 2.5
At both of these times the arrow will be 180ft high, one on the way up, the other on the way down.
2007-10-20 09:02:44 · answer #1 · answered by Mathfriend 2 · 0⤊ 0⤋
Let's take this step by step....
You know the formula:
h = -16t ^2 + 112t
You also know the height: 180 ft
You know "h" represents height
You know the variable you want is "t"
Then put it together!
180=-16t^2 + 120t
Manipulate this a little....
180=-16t^2 + 120t
180=-16t^2 + 120t
16t^2 - 120t + 180 = 0
Dos this look familier?
Put this in quadradic formula and solve for t
When you solve this formula for t, you will get two answers. Think what those answers represent and read your question again. Which one fits your question??? Pick the right one.
2007-10-20 16:05:16 · answer #2 · answered by tkquestion 7 · 0⤊ 0⤋