Imagine an XY coordinate system. Body A moves along a straight line making angle
ID: 2163465 • Letter: I
Question
Imagine an XY coordinate system. Body A moves along a straight line making angle 30 degree with the + X axis, and body B moves along a straight line making angle 45 degree to the +X axis, both bodies moving from the origin into the first quadrant. The velocity of A is 10m/sec, constant, and that of B is 20 m/sec, constant. Write the i j form of each velocity vector, and then find the i j form of the velocity of B with respect to A. Find the magnitude and direction of the velocity of B relative to A (angle to the +X axis) What will be the magnitude and direction of the velocity of A relative to B (not necessary to work out)? Find the i J components of the displacement of B revive to A at any time t, in term of t. Both bodies arc at the origin at t = 0Explanation / Answer
a) Va = 10cos(30) + 10sin(30) = 8.66i + 5j Vb = 20cos(45) + 20sin(45) = 14.14 (i+j) Vb/a = Vb - Va = 5.48i + 9.14j b) magnitude = 10.65m/sec angle = tan inverse (9.14/5.48) = 59.05 c) Va/b = -Vb/a = -5.48i - 9.14j magnitude = 10.65m/sec angle = 180 + 59.05 = 239.05 wrt to +X d) R= vdt = 5.48*t i + 9.14*t j