Answers SAgTrig4 9.1.063 A straight river flows east at a speed of 8 mi/h. A boa

Question

Answers SAgTrig4 9.1.063 A straight river flows east at a speed of 8 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The a speed of 18 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) has 60° (a) Express the velocity of the river as a vector in cotmponent form 81 +9V3jIx (b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) (c) Find the true velocity of the motorboat. (Round your answer to two decimal places.) (d) Find the true speed of the motorboat. (Round your answer to one decimal place.) 22.3 X mi/h Find the direction of the motorboat. (Round your answer to one decimal place.) N 44.3 Need Help?

Explanation / Answer

a) velocity of river as a vector in component form is given by

< 8 , 0 >

b) velocity of motorboat relative to water is

< 8 , sqrt ( 18^2 - 8^2 )>

< 8 , 2 sqrt 65 >

c) true velocity of motorboat is

< 8, 0 > + < 8 , 2 sqrt 65 >

< 16 , 2 sqrt 65 >

d) true speed of motorboat is

sqrt ( 16^2 + 2 sqrt 65^2 )

= 22.7 mi/h

e) direction is tan^-1 ( 2 sqrt 65 / 16 )

theta = 45.22

90 - 45.22 = 44.8

direction is N 44.8 E

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