1. Draw each of the following vectors, then find their x- and y-components a, d
ID: 1575161 • Letter: 1
Question
1. Draw each of the following vectors, then find their x- and y-components a, d (2.0 km, 30° left of + y-axis) b. v-(5.0 cm/s, - x-direction) c. a-(10 cm/s2, 40° left of -y-axis) 2. Starting from rest, several toy cars roll down ramps of differing lengths and angles. Rank them according to their speed at the bottom of the ramp, from slowest to fastest. Car A goes down a 6 m ramp inclined at 15°, car B goes down a 6 m ramp inclined at 20°, car C goes down 4.8 m ramp inclined at 20°, and car D goes down a 7.2 m inclined at 12. 3. Suppose E = 2A + 3B, where vector A has components Ax-5, A,-2, and vector B has components B--3, By5 a. What are the x- and y-components of vector E? b. Draw a coordinate system and in this system draw vectors A, B, and E c. What are the magnitude and direction of vector E (give direction as an angle with one of the axes, tell me which as is described in problem 1 above)?Explanation / Answer
1]
a] X component of d is:
dx = 2cos(30+90) = - 1 km
[since 30 degrees to the left of positive y axis represents the 90 degrees from + x axis to +y axis and this additional angle from +y axis].
and similarly Y component of d is:
dy = 2cos(30) = 1.732 km
b] vx = - 5 cm/s and vy = 0 cm/s
since the direction is along negative x axis.
c] 40 degrees left of negative y axis correponds to a full angle of 180+50 = 230 degrees from +x axis.
therefore, ax = 10cos230 = - 6.428 m/s2
and ay = - 10cos40 = - 7.660 m/s2.
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