# Resultant Vector using Components

## Homework Statement

A man pushing a toy car causes it to undergo 2 displacements. The first has a magnitude of 150 cm and makes an angle of 120degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees at the positive x axis. Find the magnitude and direction of the second displacement.

## The Attempt at a Solution

Displacement A + Displacement B = Displacement R
B = R - A

R = Rx + Ry
R = 140cos35i + 140sin35j

180° - 120° = 60
A = Ay + Ax
A = 150sin60j - 150cos60i (2nd Quad?? Not too sure if need to put negative here)

Hence:
B = Rx + Ry - (Ay + Ax)
B = 140cos35i + 140sin35j - (150sin60j - 150cos60i)
B = (140cos35 +150cos60)i + (140sin35 - 150sin60)j

B = sqrt( Bi^2 + Bj^2 )
B = 196

To find Direction
tetha = taninverse( (140sin35 - 150sin60)/ (140cos35 +150cos60) )
tetha = -14.65 degrees ?? weird??

HallsofIvy
Homework Helper

## Homework Statement

A man pushing a toy car causes it to undergo 2 displacements. The first has a magnitude of 150 cm and makes an angle of 120degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees at the positive x axis. Find the magnitude and direction of the second displacement.

## The Attempt at a Solution

Displacement A + Displacement B = Displacement R
B = R - A

R = Rx + Ry
R = 140cos35i + 140sin35j

180° - 120° = 60
A = Ay + Ax
A = 150sin60j - 150cos60i (2nd Quad?? Not too sure if need to put negative here)
Yes. cos(120)= -cos(60). If you are not certain of the sign leave it as cos(120) and sin(120).

Hence:
B = Rx + Ry - (Ay + Ax)
B = 140cos35i + 140sin35j - (150sin60j - 150cos60i)
B = (140cos35 +150cos60)i + (140sin35 - 150sin60)j

B = sqrt( Bi^2 + Bj^2 )
B = 196
Yes, that is correct.

To find Direction
tetha = taninverse( (140sin35 - 150sin60)/ (140cos35 +150cos60) )
tetha = -14.65 degrees ?? weird??
What is weird about it? Did you draw a picture?

• 1 person
Yes i just drew it. So -14.65 means theta is 360 - 14.65? I suck at math