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A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of your starting point will you reach the opposite bank?

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Hashirriaz830

Answer:

a) 25.5°(south of east)

b) 119 s

c) 238 m

Explanation:

solution:

we have river speed [tex]v_{r}[/tex]=2 m/s

velocity of motorboat relative to water is [tex]v_{m/r}[/tex]=4.2 m/s

so speed will be:

a) [tex]v_{m}[/tex]=[tex]v_{r}[/tex]+[tex]v_{m/r}[/tex]

solving graphically

[tex]v_{m}=\sqrt{v^2_{r}+v^2_{m/r}}[/tex]

     =4.7 m/s

Ф=[tex]tan^{-1} (\frac{v_{r}}{v_{m/r}} )[/tex]

  =25.5°(south of east)

b) time to cross the river: t=[tex]\frac{w}{v_{m/r}}[/tex]=[tex]\frac{500}{4.2}[/tex]=119 s

c) d=[tex]v_{r}t[/tex]=(2)(119)=238 m

note :

pic is attached

Ver imagen Hashirriaz830

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