Post a New Question

Discrete Math - Vectors

posted by .

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 S50°E. Represent these displacements in a vector diagram, then calculate the resultant displacement.

======

My Work:

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

-----

Then, I found the resultant displacement:

|r|² = 25² + 15² - 2(15)(25)cos130
√|r|² = √1332.1
|r| = 36.5 km

-----

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 S31.6°E

======

The textbook answer is 36.5 km S54°E




_____________________________________


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.

======

Here's my work for this question:

I drew the vectors and connected them head to tail.

-----

I tried to find the magnitude by:

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

|r|² = 10² + 6² - 2(10)(6)cos130
√|r|² = √213
|r| = 14.6

-----

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

======

Textbook answer is 7.7, 37° to vector a

  • Discrete Math - Vectors -

    I will do the second question first, since I have a question about your interpretation of S50E from the first.

    I drew the 2 unit vector to run east, then the 3 unit angle downwards to form the 50 degree angle.

    so when you construct 5a - 2b, you would draw a horizontal line 10 units long for the first part, then you must go into the opposite direction of the second vector for 6 units

    so the magnitude equation would be

    |r|² = 10² + 6² - 2(10)(6)cos50
    and r = 7.67

    now if x is the angle between the resultant and the first vector

    sinx/6 = sin50/7.67
    I got x = 36.8 degrees


    back to your first problem,
    I was always under the impression and taught that a direction like your
    S50°E meant:
    face south then 50 degrees towards the east, so I thought that the end part of your equation should have been ....cos140
    you had....cos130

    but the ....cos130 produced the answer supplied by your text, so I am confused.
    I am using the Canadian interpretation of S50°E, is it different where you are???

    Perhaps some of the other math or physics expert could help out here

  • Discrete physics -

    a body is acting upon by two force 8 newton in the direction 60degree north east.find the magnitude and the direction of the reasultant force on the body using parallel gram of vectors

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    What is the resultant of two displacement vectors having the same direction?
  2. calculus

    a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together
  3. Advanced Maths (Vectors) AQA Level, please help?

    Two ships, A and B st out from port O simultaneously. A travels due north at 16 km/h, B due east at 13 km/h. The ships radio have a rang of 120. For how long would they remain in contact if B had travelled north-east
  4. Math

    A ferry boat holds 800 people. There are 260 people already on the boat. The owner of the boat wants to load several tour groups on. The tour groups come in sizes of 40 people or 50 people. The owner would like an equal number of each …
  5. math

    a boat travels 60 km due east. it then adjusts its course by 25 degrees northward and travels another 90 km in the new direction. how far is the boat from its initial position to the nearest kilometer?
  6. math

    a boat travels 60 km due east. it then adjusts its course by 25 degrees northward and travels another 90 km in the new direction. how far is the boat from its initial position to the nearest kilometer?
  7. AP Physics C

    as she pick up her riders a bus driver traverses four successive displacements represented by the expression (-6.30 b)i-(4.00 b cos 40)i-(4.00 sin 40)j+(3.00 b cos 50)i-(3.00 b sin 50)j-(5.00 b)j here b represents one city block,a …
  8. calc

    A boat leaves a dock at 3:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 4:00 PM. How many minutes after 3:00 PM were the two boats closest together?
  9. math-mechanics 1

    i solved a)u=2i and b)r=2t+1/2[-0.4(i) 0,2(j)] at c) i don t have idea how to solve At time t = 0, a small boat is at a buoy travelling due east with speed 2 ms−1 . The boat experiences a constant acceleration of (– 0.4i + 0.1j) …
  10. Physics

    A plane travels 3 km due north, then 5 km due northeast. Represent these two displacements graphically and determine the resultant displacement by finding is magnitude and direction.

More Similar Questions

Post a New Question