Need help with solving vectors , (component form) , (magnitude, direction) , 4 part problem?

vector 1 = v1 , vector 2 = v2





Please solve all 4 if possible. Find the answers in component form (x-comp, y-comp) %26amp; in mag-dir form (magnitude, direction)





Also show me the steps in solving.





v1=(2.3 m/s, 17 degrees)


v2=(4.9m/s, 315 degrees)





a. v1 + v2





b. v1 - v2





c. -v





d. 4v2





I greatly appreciate anyone solving this for me.

Need help with solving vectors , (component form) , (magnitude, direction) , 4 part problem?
For addition problems you need to break down the vector into the x and y components of velocity, I use i for the x direction and j for the unit y axis direction. Then you just add or subtract the individual components, only mixing i with i and j with j units.





V1_x = 2.3 * cos(17) = 2.20 m/s i


V1_y = 2.3 * sin(17) = 0.67 m/s j





V2_x = 4.9*cos(315) = 3.46 m/s i


V2_x = 4.9*sin(315) = -3.46 m/s j





V1+V2 = %26lt;2.20 + 3.46, 0.67 - 3.46%26gt; = %26lt;5.66, - 2.79%26gt;





What is the magnitude? sqrt( 5.66^2 + 2.79^2) = 6.31 m/sec


What is angle, inverse Tangent (-2.79/5.66) , be carefull, and the calculator may not tell you the right quadrant, know your Trig!





Calculator say -26.2 degrees, that sound right? Draw a picture, it looks right.





On problem b is worked the same way, subtraction is just adding a negative value





problem c, direction changes, but magnitude does not, draw a picture, what angle is it, it has to be 180 degrees different.





problem d, direction is same, magnitude is 4 times original.





Please check for errors.