Sunday
April 20, 2014

Homework Help: Discrete Math - Vectors

Posted by Anonymous on Sunday, February 10, 2008 at 1:32am.

Can you please help me correct my answers for the following two questions?




1) A tour boat travels 25 km due east and then 15 km S50E. Represent these displacements in a vector diagram, then calculate the resultant displacement.

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My Work:

I drew the vectors and connected them head to tail to form a triangle.

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Then, I found the resultant displacement:

|r| = 25 + 15 - 2(15)(25)cos130
√|r| = √1332.1
|r| = 36.5 km

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Now, I'm having some problems finding the direction of the resultant displacement:

(sin50/36.5) = (sinC/25)
31.6 = C


So, I get 36.5 km S31.6E

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The textbook answer is 36.5 km S54E




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2) Vectors a and b have magnitudes 2 and 3, respectively. If the angle between them is 50, find the vectors "5a - 2b", and state its magnitude and direction.

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Here's my work for this question:

I drew the vectors and connected them head to tail.

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I tried to find the magnitude by:

5a - 2b
= 5(2a) - 2(3b)
= 10a - 6b

|r| = 10 + 6 - 2(10)(6)cos130
√|r| = √213
|r| = 14.6

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Then I tried to find the direction by:

(sinx/3) = (sin130/14.6)
x = 9.1


So, I get 14.6, 9.1 to vector a

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Textbook answer is 7.7, 37 to vector a

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