Northern Virginia community college
posted by Domynique .
A speedboat heads west at 104 km/h for 24.0 min. It then travels at 64.0° south of west at 109.0 km/h for 13.0 min.
(a) What is the average speed for the trip?
What is the average velocity for the trip?
magnitude
direction

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total distance traveled = (24/60)(104) + (13/60)(109) = 65.216666..
total time = 37 minutes = 37/60 hrs
average speed = 65.21666../(37/60) = 105.8 km/h
for the average velocity, make a vector diagram
I have a triangle ABC with AB = 41.6 , BC = 23.1666..
and angle ABC = 116°
By the cosine law:
AC^2 = AB^2 + BC^2  2(AB)(BC)cos 116°
etc
(I will let you do the arithmetic)
The direction angle would be angle BAC
since you now have all 3 sides of the triangle plus an angle you can find angle BAC by the sine law.