MATH 107 Lecture Notes - Lecture 2: Word Problem For Groups, Motorboat
14 Oct 2016
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Department
Course
Professor
Vectors
a.
iv. PropertiesofVectors
1.v. i+jFormofavector
1. Given a vector u, < a , b >, simply insert an i in front of the x, and a j in
front of t h e y , t o b e c o m e a i + b j , H a h a h a y e s , b j i s v e r y f u n n
y .
c. Vector Word Problems
i. Convert directional θ into N/S/E/W form1. Let’s say in the coordinate
plane, your final vector is 70 degrees from the x-axis. 2. Instead of
saying 70°. you would say 70° N of E.
ii. Typical Word Problem (e.g. Water and Boat problem)1. A straight
river flows east at a speed of 10 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 of 20 mi/h relative to the water.
a. Express the velocity of the river as a vector in component form.
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Document Summary
Let"s say in the coordinate plane, your final vector is 70 degrees from the x axis. Instead of saying 70 . you would say 70 n of e. Typical word problem (e. g. water and boat problem) 1. A straight river flows east at a speed of 10 mi/h. A boater starts at the south shore of the river and heads in a direction 60 from the shore. True velocity is basically the scalar speed of the boat, in addition to the speed of the water, so add the two vectors together and find the magnitude. ii. 26. 46 mph. d. find the true speed and direction of the motorboat: now that we found the true speed or velocity of the boat, we must find the angle. To do this, simply find the arctan of (10 3 / 20), which is 40. 9 . But in terms of direction, this would be written as 40. 9 n of e: resultant vectors 1.
