Pre calculus HW

Question

A straight river flows east at a speed of 12 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore. The motorboat has a speed 24 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.)

(a) Express the velocity of the river as a vector in component form.

(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.)

Find the direction of the motorboat. (Round your answer to one decimal place.)

Answer 1

24 mph at 60 degrees

12 mph at 0 degrees

construct a parallelogram and find its diagonal

use the law of cosines

d^2= 24^2 +12^2 -2(24)(12)Cos 120

d^2 = 1008

d = sqr1008 = about 31.75 mph (you know it had to be less than 24+12 =36)

to find the direction = angle use the law of sines

sin(angle)/24= sin120/31.75

sin(angle) = 24(sqr3)/2(31.75

then take the inverse sine of 12(1.732)/31.75

angle = sin^-1(.655)

= about 40.92 degrees = angle formed with the shoreline

you know it had to be less than 60 degrees