A motorboat travels across a lake at a speed of 10 mph at a bearing of 25°. The current of the lake due to the wind
is a steady 2 mph at a bearing of 340°.
a. Draw a diagram that shows the two velocities that are affecting the boat’s motion across the lake.
b. What is the resulting speed and direction of the boat?

Answer :

Answer:

a) Figure attached

b) [tex] v_r = \sqrt{3.55^2 +10.94^2}=11.50 mph[/tex]

[tex] \theta = tan^{-1} (\frac{10.94}{3.55})=72.02[/tex]

Step-by-step explanation:

Part a

See the figure attached.

Part b

For this case first we need to find the vectors of velocity for the boat and the wind like this:

[tex] b= <10 cos(65), 10 sin(65)>= <4.23, 9.06> mph[/tex]

[tex] w= <2 cos(110), 2 sin(110)>= <-0.68, 1.88> mph[/tex]

And now if we want to find the resulting velocity we just need to add the vector:

[tex] b + w = <4.23-0.68, 9.06+1.88>=<3.55, 10.94>mph[/tex]

And the resultant magnitude would be:

[tex] v_r = \sqrt{3.55^2 +10.94^2}=11.50 mph[/tex]

And if we want the resultant angle we can do this:

[tex] \theta = tan^{-1} (\frac{10.94}{3.55})=72.02[/tex]

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