What are (a) the x component and (b) the y component of a vector in the xy plane

Question

What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 172degree counterclockwise from the positive direction of the x axis and its magnitude is 8.8 m? The x component of vector is -12.6 m and the y component is +53.8 m. (a) What is the magnitude of ? (b) What is the angle (in radians) between the direction of and the positive direction of x? A room has dimensions 2.38 m (height) times 5.22 m times 6.72 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path it can take? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.) Two vectors are given by and. In unit-vector notation, find (a), (b), and (c) a third vector such that. (a) In unit-vector notation, what is the sum of and. What are (b) the magnitude and (c) the direction of (relative to )? You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-137 m, 87 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement? In the sum , vector has a magnitude of 11.1 m and is angled 37.8degree counterclockwise from the +x direction, and vector has a magnitude of 14.4 m and is angled 19.3degree counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of ? State your angle as a positive number.

Explanation / Answer

1)

x-compoennt => 8.8cos(172 deg) = -8.714

y-component => 8.8sin(172 deg) = 1.224

2)

v = -12.6 i + 53.8 j

Magnitude = sqrt(12.6^2 + 53.8^2) = 55.25 m

Direction = arctan(53.8/-12.6) = 180 - 76.82 = 103.18 degrees

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