Find the sum of the given vectors displaystyle{50}{N}angle{320}^{circ}+{170}{N}angle{150}^{circ} Rx = ? Ry = ? R = ? theta = ?

iohanetc 2020-10-25 Answered
Find the sum of the given vectors
50N320+170N150
Rx=?
Ry=?
R=?
θ=?
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Expert Answer

Luvottoq
Answered 2020-10-26 Author has 95 answers

Step 1
Assume the vectors as vector a and vector b. Represent the vectors on the graph.
a=50N320
b=170N150
image
Step 2
Now, resolve the vectors a and b to get Rx and Ry.
image
|ax|=50cos50
|ay|=50sin50
|bx|=170cos60
|by|=170sin60
Rx=|ax|+|bx|
Rx=50cos50+170cos60
Rx=52.86
Ry=|ay|+|by|
Ry=50sin50170sin60
Ry=108.92
Step 3
Finally, determine the resultant vector R and the direction theta using the resultant vectors Rx and Ry.
R=Rx2+Ry2
=(52.86)2+(108.92)2
=14657.746
=121.07
Hence, R=121.07
θ=tan1(RyRx)
=tan1(180.9552.86)
=64.11
=295.89
296
Hence, theta =296 from horizontal axis.

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