Still having problems with vectors

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In summary, the two vectors V1 and V2 are 8.94 units and 4.13 units long respectively. V1 points along the -x axis while V2 points at +35.0° to the +x axis. When calculating the components, there was an error in finding V2y, which should be 4.13sin(35) = 2.37 instead of 4.13cos(35) = 3.38. The correct components are V1x = -8.94, V1y = 0, V2x = 3.38, and V2y = 2.37. The magnitude of the sum of V1 + V2 is
  • #1
confusedaboutphysics
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Vector V1 is 8.94 units long and points along the -x axis. Vector V2 is 4.13 units long and points at +35.0° to the +x axis.
(a) What are the x and y components of each vector?
V1x =
V1y =
V2x =
V2y =
(b) Determine the sum V1 + V2.
Magnitude
________
Direction
______° (counterclockwise from the +x axis is positive)

so i know that V1x=-8.94 and V1y = 0. i did the other components, but i got them wrong. i solved for V2y by 4.13cos(35) = 3.38. then solved for V2x by 4.13sin(35) = 2.37.

So for part B i did Vx = 8.94+2.37=11.31 and Vy=0+3.38=3.38. Then found the magnitude by V=the square root of (11.31^2) + (3.38^2) = 11.80. then for the direction i did tan (angle) = 3.38/11.31=.299. the inverse of that is 16.63 degrees.

Can anyone tell me what i did wrong
 
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  • #2
confusedaboutphysics said:
so i know that V1x=-8.94 and V1y = 0. i did the other components, but i got them wrong. i solved for V2y by 4.13cos(35) = 3.38. then solved for V2x by 4.13sin(35) = 2.37.

So for part B i did Vx = 8.94+2.37=11.31 [...]

You lost the minus sign on -8.94. Minus signs count when you're adding components.
 
  • #3
ohh ok thanks! but what about the V2x and V2y components. what did i do wrong? because i got those components wrong too so i can't do part B until i finish part A...help please!
 
  • #4
Draw the triangle, with V2 as the hypotenuse.
Can you see now why V2y is not 4.13cos(35) but 4.13sin(35) ?
 
  • #5
still having trouble. so here's what i got..but i got them wrong!

V1x= -8.94
V1y = 0
V2x= 4.13cos(35) = 3.38
V2y= 4.13sin(35) = 2.37

Vx= -8.94 +3.38 = -5.56
Vy= 0 + 2.37 = 2.37

V = [the square root of (-5.56)^2 +(2.37)^2] = 6.04

tan (angle)= 2.37/-5.56 = -.426

inverse tan (-.426) = -23.09

so what did i do wrong. I got the V1x & V1y correct, but everything else wrong. PLEASE HELP!
 
  • #6
Your magnitude for V looks OK to me. What is it supposed to be?

As for the direction (angle) of V, draw a diagram that shows the x and y axes, and has Vx and Vy pointing in the proper directions, based on their signs. Look for a right triangle that has Vx and Vy as its two sides, and see where your angle of 23.09 degrees fits in (don't worry about the - sign here). From the diagram you should now be able to read off the angle that you were asked for, which is the angle measured counterclockwise from the +x axis to V.
 

1. What are vectors and why do we use them?

Vectors are mathematical quantities that have both magnitude and direction. They are used to represent physical quantities, such as velocity and force, and are essential in understanding and solving problems in physics and engineering.

2. How do I add or subtract vectors?

To add or subtract vectors, we use the head-to-tail method. This means placing the tail of one vector at the head of the other vector and then drawing a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the sum or difference of the original vectors.

3. What is the difference between vector and scalar quantities?

Vector quantities have both magnitude and direction, while scalar quantities only have magnitude. For example, velocity is a vector quantity because it has both speed (magnitude) and direction, while speed is a scalar quantity because it only has magnitude.

4. How do I find the magnitude and direction of a vector?

The magnitude (or length) of a vector can be found using the Pythagorean theorem: magnitude = √(x^2 + y^2), where x and y are the horizontal and vertical components of the vector. The direction of a vector can be found using trigonometric functions: direction = tan^-1 (y/x).

5. Can vectors be multiplied?

Yes, there are two types of vector multiplication: dot product and cross product. The dot product results in a scalar quantity, while the cross product results in a vector quantity. These operations are useful in calculating work, torque, and other physical quantities.

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