Answer:
We finally conclude that :
For the first 20 minutes ; the equation of the path following by the ferry is y = 8
After 20 minutes, Ferry turns due to south at point (-2,80
Ferry will definitely follow the vertical path passing along (-2, 8)
as such the equation for the vertical line parallel to vertical axis is in the form of x = a
Thus; teh equation of the path followed by Ferry after 20 minutes is x = -2
Step-by-step explanation:
Let's first understand our given parameters in order to solve the question
Let assume that Ballard is at the origin, then the coordinates of Ballard at origin is (0,0)
Given that Ballard is 8 miles south and 1 mile west of Edmonds.
This implies that Edmond too is 1 mile east and 8 miles north of Ballard.
The coordinates of Edmonds are (0 + 1, 0 + 8) = ( 1 , 8 )
Given that Edmonds is 6 miles due east of Kingston, so as Kingston is 6 miles due to Edmonds.
We can now say that the coordinates of Kingston are ( 1 - 6 , 8 ) = (- 5, 8 )
The sail boat is located 3 miles east and 2 miles north of Kingston, In essence; the coordinates of the sailboat are ( - 5 + 3 , 8 + 2 ) = ( -2 , 10 )
Having said and understood that;
Now; To find the equations for the lines along which the ferry is moving; we have the following;
Ferry is said to leave Kingston heading towards Edmonds at 9 mph , right? So, the initial coordinates of the Ferry will be (-5, 8)
However, after 20 minutes the coordinates turns due south!
The distance traveled by the Ferry now in 20 minutes time can thereby be calculated as:
[tex]d = 9 \ mph * \frac{20}{60} \ h[/tex]
[tex]\\\\d = 3\ miles \\[/tex]
Thus; Ferry traveled 3 miles due towards east within 20 minutes time
After 20 minutes ; the coordinates are ( - 5 + 3, 8+0) = ( -2, 8)
The equation of the line through (-5,8) and (-2,8) can therefore be represented as :
[tex]y - 8 = \frac{8-8}{-2+5}(x+5)\\\\y -8 = 0\\\\y = 8[/tex]
CONCLUSION:
We finally conclude that :
For the first 20 minutes ; the equation of the path following by the ferry is y = 8
After 20 minutes, Ferry turns due to south at point (-2,80
Ferry will definitely follow the vertical path passing along (-2, 8)
as such the equation for the vertical line parallel to vertical axis is in the form of x = a
Thus; teh equation of the path followed by Ferry after 20 minutes is x = -2
