Question

The figure shows two vectors B vector and C vector, along with their magnitudes and directions. The vector D vector is given by D vector = B vector - C vector. (a) What is the magnitude of vector D vector? (b) What angle does vector D vector make with the + x-axis? If you run a complete loop around an outdoor trade of length 400 m in 100 s, find your (a) average velocity and (b) average speed.
I need help with #18.

Answer 1

B^rightarrow = -5.6 cos 33 degree i^^- 5.6 sin 33 degree j^^C^rightarrow = 4.8 sin 22 degree j^^D^rightarrow = B^rightarrow - C^rightarrow = (-5.6 cos 33 degree i^^- 5.6 sin 33 degree j^^) - (4.8 sin 22 degree i^^- 4.8 cos 22 degree j^^) = (-5.6 cos 33 degree - 4.8 sin 22 degree) i^^+ (-5.6 sin 33 degree + 4.8 cos 22 degree) j^^= (-5.6 times 0.54 - 4.8 times 0.37) i^^+ (-5.6 times 0.54 + 4.8 times 0.93) j^^D^rightarrow = -6.48 i^^+ 1.44 j^^(b) D^rightarrow makes an theta with x - axis tan theta = 1.44/-6.48 = -0.22 theta = -12.4 degree with +ve x - axis is 347.6 degree with +ve x - axis