  A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 156 cm and makes an angle of 116° with the positive x axis. The resultant displacement has a magnitude of 151 cm and is directed at an angle of 30.0° to the positive x axis. Find the magnitude and direction of the second displacement.

Question

A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 156 cm and makes an angle of 116° with the positive x axis. The resultant displacement has a magnitude of 151 cm and is directed at an angle of 30.0° to the positive x axis. Find the magnitude and direction of the second displacement.

Step 1

Given,

Step 2

Resolving the first displacement vector, A along x and y direction and plugging the given values we get:

Step 3

Now, for Resultant vector ...

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Vectors and Scalars 