# 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.