Aman 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 126° with the positive x axis. the resultant displacement has a magnitude of 133 cm and is directed at an angle of 34.0° to the positive x axis. find the magnitude and direction (counterclockwise of the positive x axis) of the second displacement.

second displacement is  R = 208.6 cm  and  θ = 346º

Explanation:

This is a problem of adding vectors, the easiest way to work these problems is to decompose the vectors and find the resulting vectors on each axis

Let's use trigonometry to break down each displacement vector. Let's start with vector 1 that has a magnitude m1 = 156 cm

          sin 126 = Y1 / m1

          Y1. = m1 without 126

          Y1 = 156 without 126

          Y1 = 126.2 cm

          cos 126 = X1 / m1

          X1 = m1 cos 126

          X1 = 156 cos 126

          X1 = - 91.69 cm

The resulting vector has R = 133 cm

         sin 34 = Ry / R

         Ry = R sin 34

         Ry = 133 sin 34

         Ry = 74.37 cm

         cos 34 = Rx / R

         Rx = R cos 34

         Rx = 133 cos 34

         Rx = 110.3 cm

We already have all the components, we can add algebraically on each axis

X axis

         Rx = X1 + X2

         X2 = Rx -X1

         X2 = 110.3 - (-91.69)

         X2 = 202 cm

Y Axis  

         Ry = Y1 + Y2

         Y2 = Ry - Y1

         Y2 = 74.37 -126.3

         Y2 = -52 cm

Let's build the resulting vector

          R = (202 i ^ + 52 y ^) cm

          R = (202, -52) cm

We can also use the Pythagorean triangle and trigonometry to find the module and direction

          R² = Rx² + Ry²

          R = √(202² + 52²)

          R = 208.6 cm

          tan θ = Ry / Rx

          tan θ = -52/202

          θ = tan⁻¹ (-0.257)

          θ = -14.4º

The negative sign indicates that it is measured from the x-axis clockwise, to measure counterclockwise from the x-axis

          θ = 360-14

           θ = 346º

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

nah.   i'm just sleepy.