A straight river flows east at a speed of 10 mh A boater sta

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

Solution

a)velocity of river ,v_rg=10 i

b)velocity of boat with respect to water ,v_br=24(cos60^oi+sin60^oj)

v_br=(12i+123j)

v_br=(12i+20.78j)

c)true velocity of boat =v_bg

v_bg=v_br+v_rg

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

v_bg=(22i+123j)

v_bg=(22i+20.78j)

d)true speed of boat=|v_bg|

true speed of boat=[(22)²+(123)²]

true speed of boat=30.3 mi/hr

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

direction = N46.6^oE