Answer:
Step-by-step explanation:
Let's suppose that Ballard is an origin with coordinates (0;0)
Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.
Thus, coordinates of Edmonds (0+1; 0+8) (1;8)
Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds
Thus, Kingston coordinates (1-6;8) (-5:8)
Sailboat is 3 miles east and 2 miles north of kingston
So, coordinates of sailboat are (-5+3; 8+2) (-2;10)
a)
Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.
Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)
After 20 minutes the ferry turns to south.
This distance travelled (20min) is d=9mph*20/60h=3 miles
So, ferry travelled 3 miles toward east in 20 min
Then, coordinates became (-5+3;8+0) (-2;8)
Thus, we have a line connecting two points (-5;8) and (-2;8)
Line connecting them has an equation:
y-8 = (8-8)/(-2+5) * (x+5)
y-8=0
y=8 - This is the equation for the first 20 minutes of travel
Then, ferry turns due south (-2;8) and has a vertiacl line
The equation of verical line is x=a, so the equation will be x=2
b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.
region looks like a circular disc with a center (-2;10)
(x+2)^2+(y-10)^2=3^2
(x+2)^2+(y-10)^2 <9 (interior of the circular disc)
(x+2)^2+(y-10)^2 >9 (exterior)
The equation of the line joining the Kingston and Edmonds is y=8
the point of intersection:
(x+2)^2+(8-10)^2=9
(x+2)^2=5
x is approximately 0.24; -4.24
(0.24;8) (-4.24;8) - intersection points
c) The ferry exits the radar during the trid due south long x=-2
The points of intersection of the circle and the line x=-2:
(-2+2)^2+(y-10)^2=9
0+(y-10)^2=0
y is 7.13
(-2;7)
d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone
Speed is 9mph
The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min
So, it exists after 6.67 minutes
e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)
The distance travelled is = [-4.24+2]=2.24 miles
The time taken to cover these miles is = t=2.24/9 *60=14.93 min
After turning to south ferry remains in radar for 6.7 min
So, it remains in radar zone for 14.93+6.7=21.63min
.
---> equation (1)
---> equation (2)
substitute this value in equation (1) then