Imposing Coordinates Homework: Eriks & Ferrys Positions & Distances

[PhysicslyDSBL]

Homework Statement

Eriks disabled boat is floating at a stationary location 3 miles East and 2 miles North of Kingston. A ferry leaves Kingston heading due East towards Edmonds at 12mph. Erik leaves the sailboat in a dingy heading due South at 10ft/sec (hoping to intercept the ferry). Edmonds is 6 miles due East of Kingston.

a) Compute Eriks spead in mph and the ferrys speed in ft/sec.
b) Impose a coordinate system of Erik and the ferry. What are Eriks and the ferrys locations at time 0, 30sec, 7min, and 1 hour? What are the distances between them at each time-point?
c) Explain why Erik misses the ferry.
d) After 10 minutes a Coast Guard boat leaves Kingston heading due East at a speed of 25ft/sec. Will the Coast Gaurd boat catch the ferry before it reached Edmonds? Explain.

Homework Equations

distance = rate X time
d=sqrt (x2-x1)^2 - (y2-y1)^2

The Attempt at a Solution

a) Eriks speed is 10ft/sec or 6.818 mph
The ferrys speed is 12mph or 17.604 ft/sec
b)Eriks orgin is (3,2)
Ferry orgin is (0,0)

I am confused with how to use the coordinates to calculate their positions at certain time-points.

I think to find the distances between them at the given time-points I use the following equations and substitute them into the distance formula:
Erik: (3, 2-6.818) Ferry: (12,0)

Any help is appreciated!

 

[Mark44]

Homework Statement

Eriks disabled boat is floating at a stationary location 3 miles East and 2 miles North of Kingston. A ferry leaves Kingston heading due East towards Edmonds at 12mph. Erik leaves the sailboat in a dingy heading due South at 10ft/sec (hoping to intercept the ferry). Edmonds is 6 miles due East of Kingston.

a) Compute Eriks spead in mph and the ferrys speed in ft/sec.
b) Impose a coordinate system of Erik and the ferry. What are Eriks and the ferrys locations at time 0, 30sec, 7min, and 1 hour? What are the distances between them at each time-point?
c) Explain why Erik misses the ferry.
d) After 10 minutes a Coast Guard boat leaves Kingston heading due East at a speed of 25ft/sec. Will the Coast Gaurd boat catch the ferry before it reached Edmonds? Explain.

Homework Equations

distance = rate X time
d=sqrt (x2-x1)^2 - (y2-y1)^2

The Attempt at a Solution

a) Eriks speed is 10ft/sec or 6.818 mph
The ferrys speed is 12mph or 17.604 ft/sec
b)Eriks orgin is (3,2)
Ferry orgin is (0,0)

I am confused with how to use the coordinates to calculate their positions at certain time-points.

I think to find the distances between them at the given time-points I use the following equations and substitute them into the distance formula:
Erik: (3, 2-6.818) Ferry: (12,0)

Any help is appreciated!

As you pointed out, d = r*t, so you need to represent Erik's and the ferry's positions at time t. To get you started, Erik's position at time t (in hours) is (3, 2 - 6.818*t). You need to find the ferry's position at time t and calculate the distance between these points. Presumably, at some value of t, the distance will be 0.

 

[Mark44]

By the way, are you at EdCC or maybe ShorelineCC?