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

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 magnitude6.45cm and direction 63.2? 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 6.45cm , but a direction 22.3? measured in the sense from the +x-axis toward the +y-axis.

1- Find the component Ax of A? .

2- Find the component Ay of A?

3-Find the magnitude of A? .

4-Find the direction of A?  measured in the sense from +x - axis toward the +y - axis.

Explanation / Answer

C=6.45Cos 22.3i + 6.45Sin 22.3 j

B=6.45Cos63.2 i -6.45 Sin 63.2 j

C=A+B

A=C-B=3.06i +8.20j

Ax=3.06

Ay=8.20

magnitude of A=sqrt(8.20^2+3.06^2)=8.75cm

direction=tan^-1(8.20/3.06)=69.5 degrees towards +y from +x

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