A passenger walks from one side of a ferry to the other as it approaches a dock.

Question

A passenger walks from one side of a ferry to the other as it approaches a dock.Passenger's velocity is 1.55m/s due north relative to the ferry, and 4.60m/s at an angle of 30.0 ?west of north relative to the water.

A.What is the magnitude of the ferry's velocity relative to the water?

B.What is the direction of the ferry's velocity relative to the water?

Also,

Vector A?  points in the negative x direction and has a magnitude of 22 units. The vector B?  points in the positive y direction.

Sketch A?  and B? .

Draw the vectors with their tails at the dot. Must have correct orientation and exact length.

Explanation / Answer

This is best explained by realizing it is done by adding vectors and using the cos law for distances.

Step One
=======
Draw the diagram. You have to follow my directions, because a diagram is impossible to draw.

a. Start with a point on the page. Label that point as start.
b. Draw your first vector straight up the page (north) Put an arrowhead on the point furthest away from start. Label the vector 1.55 m
c. Draw your second vector heading off at an angle of 30 west of north from the arrow end of the first vector. Put an arrowhead at the end of the second vector.
d. Go from start to the end of the second vector. That vector is what you need to know.

Step 2
=====
What is the angle between the two vectors (answer 150 -- see if you can get it).

Step 3
=====
Solve for the magnitude of the ferry's velocity using the cos law.

a^2 = b^2 + c^2 - 2bc*cos(A)
a=??
b= 4.6 m/s
c= 1.55 m/s
A=150 degrees.

a^2 = 4.6^2 + 1.55^2 - 2*4.6*1.55*cos(150)
a^2 = 21.16 + 2.4025+12.34
a^2 = 35.9025
a = sqr(35.9025)
a = 5.99 to the right number of sig digs.

Step 4
====
find the angle
A = 150 degrees
a = 5.99
b = 4.6
B = ???

I am not in love with the sign law because it has an ambiguous case, but this is not it. You could use the cos law but there is a lot of calculation involved.

Sin(A) ...........Sin(B)
====....= ....=====
a .....................b

Sin(150)..........Sin(B)
====== = ....=======
5.99.................4.6

Sin(B) = 2.3/5.99 = .383
B=sin-1(0.383)
B = 22.57 degrees

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