Question 860457: You are flying a plane at a height of 1500m, when you spot a squirrel 500m directly below you fall from a cliff. The squirrel falls according to this data, and continues to fall with the same acceleration towards the ground (not a linear pattern):
(X, Y)
(Time (s), height above the ground (m))
(0, 1000)
(1, 995)
(2, 980)
(3, 955)
Assuming that you can turn your plane instantaneously and fly directly downwards at 100m/s to try and save the squirrel, determine at what height and what time you catch the squirrel. (Don't worry, you will be able to save him)
-
What I know: my plane is going to be represented by a linear pattern and the squirrel will be represented by a parabola. I first need to find the equations of both lines and then I need to find the point where the two intersect.
PLEASE HELP!! THANK YOU!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! You are flying a plane at a height of 1500m, when you spot a squirrel 500m directly below you fall from a cliff. The squirrel falls according to this data, and continues to fall with the same acceleration towards the ground (not a linear pattern):
(X, Y)
(Time (s), height above the ground (m))
(0, 1000)
(1, 995)
(2, 980)
(3, 955)
Assuming that you can turn your plane instantaneously and fly directly downwards at 100m/s to try and save the squirrel, determine at what height and what time you catch the squirrel.
:
Find the linear equation for plane heading straight down
y = 1500 - 100x
:
Find the equation for the falling animal
y = ax^2 + 1000
Using the given data, find the value of a when x = 1 and y = 995
a(1^2) + 1000 = 995
a = 995 - 1000
a = -5
Y = -5x^2 + 1000 is the equation for the animal
You can check this using x=2, find y see if it agrees with the data.
y = -5(2^2) + 1000
y = -20 + 1000
y = 980
You can check it for x=3
:
When the plane reaches the animal:
animal ht = plane ht
-5x^2 + 1000 = 1500 - 100x
-5x^2 + 100x + 1000 - 1500 = 0
-5x^2 + 100x - 500 = 0
simplify, divide by -5
x^2 - 20x + 100 = 0
Factors to
(x-10)(x-10) = 0
x = 10 seconds they should be at the same height
Find the height
y = 1500 - 100(10)
y = 500 ft height of the plane
Check the height of the squirrel at 10 sec
y = -5(10^2) + 1000
y = -500 + 1000
y = 500 ft too
:
Intersection: x=10, y=500
|
|
|
