How Do I Find Vector Components Using Trigonometric Formulas?

In summary, the problem involves finding vector components using trigonometric formulas. The initial velocity has both vertical and horizontal components, and the angle can be assigned a name to solve for it using equations of motion. There are two angles because the range of values for sin x increases as you move away from 0 and 90 degrees. The physical reason for this is unknown, but it is simply a mathematical concept.
  • #1
meganw
97
0
Vector Angle Problem - Answered, thanks! =)

1. The problem statement

Find Vector Components

Homework Equations



trig formulas are important here: sin =o/h, cos=a/h, tan=o/a

The Attempt at a Solution



Thanks for the help! =)
 
Last edited:
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  • #2
meganw said:
Is 7.6 the initial vertical velocity? Or horizontal? Sorry I'm just confused.

It's just initial velocity, which has both vertical and horizontal components.
 
  • #3
But how do I find those components if I don't know the angle?
 
  • #4
Just assign the angle some name, like [itex]\theta_0[/itex]. Then with the given info and the equations of motion, solve for [itex]\theta_0[/itex].
 
  • #5
Thank you so much!
 
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  • #6
meganw said:
Thank you so much! I didn't realize I could do that sort of thing...thanks again! =)

Is there any "physics" reason why there are 2 angles...mathematically sin x = 1.5 at various values of x...

sin x must be between 0 and 1...

Actually there's one way to think about why there are two angles... Think about the range when the angle is 0 and the angle is 90... in both cases the range is 0. so the range gets larger as you go up from 0... and as you go down from 90... so that gives an intuitive reason why there are two angles for each range... for a particular range... if you have an angle close to 0... then there's another angle close to 90...

When you solve for [tex]\theta_0[/tex] two solutions will appear... note: you're restricted to angles between 0 and 90.
 
  • #7
meganw said:
Is there any "physics" reason why there are 2 angles...mathematically sin x = 1.5 at various values of x...

I do not know the "physical reason" behind it. But since we are talking about angles and distances, I guess I will resort to saying "the math works that way." :)
 
  • #8
Wow, thanks both of you! I really appreciate it, you have no idea! =)
 

1. What is the Vector Angle Problem?

The Vector Angle Problem is a mathematical problem that involves finding the angle between two vectors in a given coordinate system. This problem is commonly encountered in physics and engineering applications.

2. How do you calculate the angle between two vectors?

To calculate the angle between two vectors, you can use the dot product or cross product formula. The angle can be found by taking the inverse cosine of the dot product divided by the product of the magnitudes of the two vectors. Alternatively, you can use the cross product formula to find the sine of the angle and then take the inverse sine to find the angle.

3. What is the difference between the dot product and cross product?

The dot product is a scalar quantity that results in a single number. It is calculated by multiplying the magnitudes of two vectors and the cosine of the angle between them. The cross product is a vector quantity that results in a vector perpendicular to the two input vectors. It is calculated by taking the product of the magnitudes of the two vectors and the sine of the angle between them.

4. Can the angle between two vectors be negative?

No, the angle between two vectors is always positive. This is because the dot product and cross product formulas will always yield a positive value for the angle. If a negative angle is found, it means that an incorrect calculation has been made.

5. What are some real-world applications of the Vector Angle Problem?

The Vector Angle Problem has numerous applications in physics and engineering, such as in determining the trajectory of a projectile, calculating the tension in a rope, analyzing the forces acting on an object, and designing structures and machines. It is also used in computer graphics and animation to create realistic 3D models.

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