Flight Patterns
By: Saumya Naik
The Situation
Variables
Variable Y - Height from ground (meters)
Hawk
Hummingbird
Equation for Hummingbird
- Y2- Y2 / X2-X1= slope
- 20-16/2-0= slope (sub in the given points)
- 4/2= slope
- 2=slope
Now find the value of b using y=mx+b
- y= mx+b
- y=2x+b
- 16=2(0) + b (sub in given point (0,16) to find the value of b)
- 16=b
Therefore the equation is y= 2x+16
Equation for Hawk
- Y2-Y1 / X2-X1 = slope
- 90-100 / 2-0 = slope (sub in the given points)
- -10 / 2 = slope
- -5 = slope
Find the value of b using y= mx+b
- y= mx+b
- y= -5x+b
- 100= -5(0) +b (sub in given point (0,100) to find the value of b)
- 100=b
Therefore the equation is y= -5x + 100
Graph
Close up of Intersection
Hummingbird in blue
Method 1: Graphing
After graphing both lines you can see that both birds will meet at 12 seconds and both birds will be 40m above ground
Method 2 substitution:
-5x+100= 2x+16
100-16=2x+5x
84=7x
84/7= x
12=x
Now sub one given point.
y= 2(12) +16
y= 24+16
y= 40
So the point is (12,40)
Meaning that they will meet at 12 seconds at the height of 40m above ground
Summary
Which bird will reach it's goal first?
Looking at the graph you can tell that the hawk will catch his prey before the hummingbird catches up with its flock. The hawk will reach it's prey 2 seconds earlier than the bird reaches it's goal. The hawk flies faster than the hummingbird.