Suppose three teams play a tug-of war game. Team A tugs with force 200 units at

Question

Suppose three teams play a tug-of war game. Team A tugs with force 200 units at an angle of 0 degree, team B tugs with force of 350 units at an angle of 150 degree, what vector C is needed so that no team wins? In other words, find a vector so that when A + B + C is zero. Use trigonometry and vector ideas to answer steps (1) thru (5) below. Step (1) What is A vector ? A vector = ______ i + ______ j Step (2) What is B vector? B vector = ______ i + ______j Step (3) What is the resultant A vector + B vector ? A vector + B vector = ______ i + _____j Step (4) what is the antiresultant - (A vector + B vector)? -(A vector + B vector) = ____ i + _____j Step (5) What is the magnitude of the antiresultant _____ What is the angle in standard position ______

Explanation / Answer

From the given question,

Step 1 : A= 200 i + 0j

Step 2: B=350 cos150 i + 350 sin150j

Step 3 : A + B

=200 i + 0j + 350 cos150 i + 350 sin150j

=(200 + 350 cos150)i + 350 sin150j

anti resultant= -(A+B)

=-(200 + 350 cos150)i - 350 sin150j

anti resultant(C) = 103.1 i + -175j

magnitude of anti resultant= 203 units

angle= tan-1(-175/103.1)= - 59.5 degrees wrt x axis.

or 59.5 degrees in clockwise direction.

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