2. A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found u
sing the function f(x) = −1.5x + 69, where x is the time in seconds the airplane has been in the air.
a. Draw the graph of the function
b. How many seconds did it take the paper airplane to reach the ground?
c. Explain your answer.
a. Draw the graph of the function
b. How many seconds did it take the paper airplane to reach the ground?
c. Explain your answer.
2 answers:
Answer:
It takes 46 seconds for the plane to reach the ground.
Step-by-step explanation:
We are given the following in the question:
The height of the paper airplane above the ground is given by a function:
where f(x) is the height above the ground and x is the time in seconds.
a) The attached image shows the graph for the given equation.
As clear from the graph the unction has a y-intercept of 69 and x-intercept of 46.
b) We have to find the time taken by he plane to reach the ground.
The height of plane on ground is 0
Thus, we can write:
c) Thus, it takes 46 seconds for the plane to reach the ground from the top of the tall building to reach a height of 0.
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Answer:
a) starting height: 5.5 ft
b) hang time: 5.562 seconds
c) maximum height: 126.5 ft
d) time to maximum height: 2.75 seconds
Step-by-step explanation:
a) The starting height is the height at t=0.
h(0) = -16·0 +88·0 +5.5
h(0) = 5.5
The starting height is 5.5 feet.
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b) The ball is in the air between t=0 and the non-zero time when h(t) = 0. We can find the latter by solving ...
-16t^2 + 8t +5.5 = 0
t^2 -(11/2)t = 5.5/16 . . . . . subtract 5.5, then divide by -16
t^2 -(11/2)t +(11/4)^2 = (5.5/16) +(11/4)^2 . . . . complete the square
(t -11/4)^2 = 126.5/16 . . . . . . . . . . . . . . . . . . . . call this [eq1] for later use
t -11/4 = √7.90625
t = 2.75 +√7.90625 ≈ 5.562
The ball will be in the air about 5.562 seconds.
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c) If we multiply [eq1] above by -16 and add the constant on the right, we get the vertex form of the height equation:
h(t) = -16(t -11/4) +126.5
The vertex at (2.75, 126.5) tells us ...
The maximum height of the ball is 126.5 feet.
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d) That same vertex point tells us ...
The maximum height will be reached at t = 2.75 seconds.
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If you really need answers fast, a graphing calculator can give them to you in very short order (less than a minute).
