2D motion finding displacement direction and velocity

In summary, the problem involves calculating the magnitude and direction of displacement and velocity for a person walking in three directions with given distances and times. The equations used are r=xx^+yy^ for displacement and v=r/t for velocity. The hatted characters signify the direction of the components. The magnitude of displacement can be found using the Pythagorean theorem with the x and y components as the legs of the triangle. To find the direction, the inverse tangent of y divided by x can be used, with attention to the signs of the components.
  • #1
u0467750
4
0

Homework Statement


some one walking three directions 0.35 east then 0.75 south then 2.95 33 degrees north of west. The whole trip took 2 hours. Magnitude and direction of displacement as well as the magnitude and direction of velocity.


Homework Equations


r (displacement vector) x (I think in the equation it's the x components) y ( y components) a and I am confused with the x^ and y^ the hats are supposed to be on top. The equation is r=xx^+yy^ where x=d1-d3cos(theta) and where y=-d2+d3sin(theta) where the d's are distance one = 03.5 distance two =0.75 and distance 3 = 2.95


The Attempt at a Solution


so I solved the equations of x and y and for x I got -2.124 then for y I got 0.856 then I pluged those into the other equation and got 1.606 which i thought would be the magnitude but it was not correct and I don't really know what to do with the x^ and y^ or how to find the direction of this displacement any help would be great
 
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  • #2
Actually showing your work step by step for how you got your anwers would be helpful.
 
  • #3
ok so for the x equation I put x=0.35-2.95(cos(33)) then I put that in my calculator and got the answer I gave then for the y equation I did y=-0.75+2.95(sin(33)) and got y=0.856 then in the other equation where I'm finding r I just added those two numbers together because I don't know what to do with the x and y hats . . . I am retarded
 
  • #4
u0467750 said:
ok so for the x equation I put x=0.35-2.95(cos(33)) then I put that in my calculator and got the answer I gave then for the y equation I did y=-0.75+2.95(sin(33)) and got y=0.856 then in the other equation where I'm finding r I just added those two numbers together because I don't know what to do with the x and y hats . . . I am retarded

You're not retarded. Don't say that.

The hatted characters are just there to indicate the direction of the component of the vector. In the 2D case, the magnitude is found by using the pythagorean theorem with the components you found as the legs of the triangle. It should be smooth sailing from there.
 
  • #5
ok so I used the pythagorean theorem and got the right answer for the magnitude of the displacement, but how do I find the direction of the displacement
 
  • #6
and I found the velocity but also do not know how to find the direction is it the inverse tangent of the angle 33 with the x and y components I found?
 
  • #7
It's the inverse tangent of y divided x. Be sure you have the correct signs on the components.
 

FAQ: 2D motion finding displacement direction and velocity

1. What is 2D motion?

2D motion refers to motion that occurs in two dimensions, typically represented by the x and y axes. This can include both horizontal and vertical movement.

2. How do you calculate displacement in 2D motion?

Displacement in 2D motion can be calculated by finding the change in position in both the x and y directions. This can be done using the Pythagorean theorem, where displacement is equal to the square root of the sum of the squared changes in position in each direction.

3. How do you determine the direction of an object's motion in 2D?

The direction of an object's motion in 2D can be determined by looking at the changes in position in each direction. If the change in the x direction is greater than the change in the y direction, the motion is primarily in the x direction. If the change in the y direction is greater, the motion is primarily in the y direction. If the changes in both directions are equal, the motion is at a 45-degree angle.

4. What is velocity in 2D motion?

Velocity in 2D motion refers to the rate of change of an object's position in both the x and y directions. It is a vector quantity that includes both magnitude (speed) and direction.

5. How do you calculate velocity in 2D motion?

Velocity in 2D motion can be calculated by dividing the change in position in each direction by the change in time. This will give you the velocity in both the x and y directions, which can then be combined using the Pythagorean theorem to find the overall velocity magnitude and direction.

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