A straight river flows east at a speed of 10 m/h. A boater starts at the south s

Question

A straight river flows east at a speed of 10 m/h. A boater starts at the south shore of the river and heads in a direction 60 degree from the shore (see the figure). The motorboat has a speed of 24 ml/h relative to the water. (Assume that the i vector points east, and the j vector points north.) Express the velocity of the river as a vector in component form. ____ Express the velocity of the motorboat relative to the water as a vector in component form. _____ Find the true velocity of the motorboat _____ Find the true speed of the motorboat ____ ml/h Find the direction of the motorboat N _____ * E

Explanation / Answer

a)velocity of river ,vrg=10 i

b)velocity of boat with respect to water ,vbr=24(cos60oi+sin60oj)

vbr=(12i+123j)

vbr=(12i+20.78j)

c)true velocity of boat =vbg

vbg=vbr+vrg

vbg=(12i+123j)+(10 i)

vbg=(22i+123j)

vbg=(22i+20.78j)

d)true speed of boat=|vbg|

true speed of boat=[(22)2+(123)2]

true speed of boat=30.3 mi/hr

direction = N(90o-tan-1(123/22))E

direction = N46.6oE

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