What are the a) x components of a verctor a in the xy plane if its direction is 250 degrees counterclockwise from the positive direction of the x axis and its magnitude is 7.3m?
b) the same question as above but for the y component of the vector a.
In the book it says that the answer for a) is -2.5m
b)-6.9m
I can't seem to get these answers. Can you help me?
Measuring the angle the way you specified:
xcomponent= Mag*cosTheta
Ycomponent= Mag*sinTheta
The book seems to be in agreement with this.
Yes, you are on the right track with using the formulas xcomponent = Mag*cosTheta and ycomponent = Mag*sinTheta. Let's break down the steps to find the x and y components of the vector in the xy plane:
Given:
- Magnitude of vector a: 7.3m
- Direction of vector a: 250 degrees counterclockwise from the positive x-axis
a) To find the x component:
Step 1: Convert the direction from degrees to radians.
Angle in radians = 250 degrees * π/180 ≈ 4.36 radians
Step 2: Apply the formula xcomponent = Mag * cos(theta).
xcomponent = 7.3m * cos(4.36) ≈ -2.496m
Rounding to one decimal place, the x component is approximately -2.5m.
b) To find the y component:
Step 1: Convert the direction from degrees to radians (as done in step 1 of part a).
Step 2: Apply the formula ycomponent = Mag * sin(theta).
ycomponent = 7.3m * sin(4.36) ≈ -6.906m
Rounding to one decimal place, the y component is approximately -6.9m.
So the correct answers for the x and y components are:
a) x component: -2.5m
b) y component: -6.9m
Note: Sometimes, due to rounding errors or different methods in textbooks, there might be slight variations in the final calculated values, but they should be very close.