Chapter03 - 1. A vector a can be represented in the...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
1. A vector a G can be represented in the magnitude-angle notation ( a , θ ), where 22 x y aa a =+ is the magnitude and 1 tan y x a a §· = ¨¸ ©¹ is the angle a G makes with the positive x axis. (a) Given A x = 25.0 m and A y = 40.0 m, ( 25.0 m) (40.0 m) 47.2 m A =− + = (b) Recalling that tan = tan ( + 180°), tan –1 [(40.0 m)/ (– 25.0 m)] = – 58° or 122°. Noting that the vector is in the third quadrant (by the signs of its x and y components) we see that 122° is the correct answer. The graphical calculator “shortcuts” mentioned above are designed to correctly choose the right possibility.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. The angle described by a full circle is 360° = 2 π rad, which is the basis of our conversion factor. (a) () 2r a d 20.0 20.0 0.349 rad 360 π °= ° = ° . (b) 2 r a d 50.0 50.0 0.873 rad 360 ° = ° . (c) r a d 100 100 1.75 rad 360 ° = ° . (d) 360 0.330 rad = 0.330 rad 18.9 r a d ° . (e) 360 2.10 rad = 2.10 rad 120 r a d ° . (f) 360 7.70 rad = 7.70 rad 441 r a d ° .
Background image of page 2
3. The x and the y components of a vector G a lying on the xy plane are given by cos , sin xy aa θθ == where || = G is the magnitude and θ is the angle between G a and the positive x axis. (a) The x component of G a is given by a x = 7.3 cos 250° = – 2.5 m. (b) and the y component is given by a y = 7.3 sin 250° = – 6.9 m. In considering the variety of ways to compute these, we note that the vector is 70° below the – x axis, so the components could also have been found from a x = – 7.3 cos 70° and a y = – 7.3 sin 70°. In a similar vein, we note that the vector is 20° to the left from the – y axis, so one could use a x = – 7.3 sin 20° and a y = – 7.3 cos 20° to achieve the same results.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. (a) The height is h = d sin θ , where d = 12.5 m and = 20.0°. Therefore, h = 4.28 m. (b) The horizontal distance is d cos = 11.7 m.
Background image of page 4
5. The vector sum of the displacements G d storm and K d new must give the same result as its originally intended displacement o ˆ (120 km)j d = G where east is # i , north is # j. Thus, we write storm new ˆˆ ˆ (100 km)i, i j. dd A B == + GG (a) The equation storm new o d += G readily yields A = –100 km and B = 120 km. The magnitude of G d new is therefore equal to 22 new | | 156 km dA B =+ = G . (b) The direction is tan –1 ( B / A ) = –50.2° or 180° + ( –50.2°) = 129.8°. We choose the latter value since it indicates a vector pointing in the second quadrant, which is what we expect here. The answer can be phrased several equivalent ways: 129.8° counterclockwise from east, or 39.8° west from north, or 50.2° north from west.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6. (a) With r = 15 m and θ = 30°, the x component of G r is given by r x = r cos = (15 m) cos 30° = 13 m. (b) Similarly, the y component is given by r y = r sin = (15 m) sin 30° = 7.5 m.
Background image of page 6
(a) We compute the distance from one corner to the diametrically opposite corner: 222 (3.00 m) (3.70 m) (4.30 m) ++ . (b) The displacement vector is along the straight line from the beginning to the end point of the trip. Since a straight line is the shortest distance between two points, the length of the path cannot be less than the magnitude of the displacement.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/11/2010 for the course PHYS 2101,2102 taught by Professor Giammanco during the Spring '10 term at LSU.

Page1 / 74

Chapter03 - 1. A vector a can be represented in the...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online