You are to program a robotic arm on an assembly line to move in the xy-plane. It

Question

You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A ; its second displacement is B , of magnitude 6.41 cm and direction 62.6 measured in the sense from the +x-axis toward the -y-axis. The resultant C =A +B of the two displacements should also have a magnitude of 6.41 cm , but a direction 21.6 measured in the sense from the +x-axis toward the +y-axis.Find the component Ax of A .Find the component Ay of A .Find the magnitude of A .Find the direction of A measured in the sense from +x - axis toward the +y - axis.

Explanation / Answer

B = 6.41 ( cos62.6i + sin62.6j) = 2.95i + 5.69j cm

C = 6.41(cos21.6i + sin21.6j) = 5.96i + 2.36j cm

and given that C = A +B

5.96i + 2.36j = A + 2.95i + 5.69j

A = 3.01i - 3.33j

Ax = 3.01 cm .......Ans

Ay = -3.33 cm .......Ans

magnitude = sqrt(3.01^2 + 3.33^2) = 4.49 cm

direction = 360 -tan^-1(3.33/3.01) = 312.11 deg

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