4) Your boat is moving at a speed of 15 miles per hour at an angle of 25° upstre

Question

4) Your boat is moving at a speed of 15 miles per hour at an angle of 25° upstream on a river flowing at 4 miles per hour. The situation is illustrated in the figure below. Wster's peed: 4 miles per bour 15 miles per heur Beat's velecity relative to the gred a. Find the vector representing your boat's velocity relative to the ground. b. What is the speed of your boat, to the nearest mile per hour, relative to the ground? c. What is the boat's direction angle, to the nearest tenth of a degree, relative to the ground?

Explanation / Answer

speed of boat = 15 miles / hour

angle upstream = 25 degrees

velocity vector with respect to river = 15 cos 25 i + 15 sin 25 j

= 13.59i + 6.34 j

velocity relative to ground = 17.59 i + 6.34 j

b) speed of the boat = sqrt ( 17.59^2 + 6.34^2 )

= 18.70 miles / hour

c) boats direction angle = tan^-1 ( 6.34 / 17.59 )

= 19.8 degrees

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