Expert: Sherry Wallin - 1/20/2010

Question
1.   #68a plane with an airspeed of 450 miles per hour is flying in the direction N35degW. Round components to the nearest 10th and express vector in terms of (i) and (j).

2.   #52the components of v=180i+450j represent the respective number of one day and three  day videos rented from a video store. The components of w=3i+2j represent the prices to rent the one day and three day videos respectively. Find v*w and describe what the answer means in practical terms.

3.   A vector has the following initial and terminal points respectively: Initial point (-1,2), terminal point (4,6). What is the position vector?

4.   A football quarterback throws the football with a speed of 48 ft./sec. at an angle of 45 deg. Upward from the ground. The vector that describes the motion of the football is?

5.   In which quadrant is the terminal point of the vector v=6i-10j

6.   The vector (v) is multiplied by the following scalar. In which quadrant will the terminal point of the product vector be? V=2i+2j; -2(v)


Answer
Hi Neal~
    When wanting help with questions, try explaining what you have tried and what you don't understand instead of just listing a set of problems. I will help you through a couple of them.

#1 The N35degW means that you are 90 + 35 deg from the initial x axis so the reference angle is 180 -125 = 55 deg. You have a right triangle in the 2nd quadrant with a reference angle of 55 deg and the angle across from the x axis is 35 deg because 35 + 55 = 90. Your airspeed of 450 mph is the magnitude of the vector which in this case is your hypotenuse of the right triangle. So you have sin 55 deg = y/450 and cos 35 deg = x/450  which implies that 450*sin 55 deg = y and
450*cos 35 deg = x. See if you can finish the problem with this information.


#3 One way of dealing with this problem is to translate the vector so it is originating from the origin (0,0). This is because if the length of the vector is maintained as well as the angle the vector makes with the initial (x) axis they are all the 'same' vector. (In other words, all vectors of the same length that are parallel to one naother are essentially considered to be the same vector). To translate from (-1,2) to (0,0) you need to move 1 unit to the right and 2 units down. Do that to both the initial point and the terminal point. This will give you (0,0) as the initial point and (5,4) for the terminal point. You can check this by verifying that the magnitudes are the same and the angles are the same. See if you can finish the problem with this information.

#5 In what quadrant is x positive and y negative? That is the quadrant this vector is in.

#6 -2(v) = -4i -4j. Where are x and y both negative? That is where this vector lies (including it's terminal point).

Math Prof