Calculating Weight Component on Hillside | Trig/Physics Homework Question

  • Thread starter maff is tuff
  • Start date
In summary, the new angle is alpha because it is the only angle that satisfies the equation w=sin(alpha).
  • #1
maff is tuff
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1

Homework Statement



A boulder of weight w rests on a hillside that rises at a constant angle (alpha) above the horizontal, as shown in the figure. The boulder's weight is a force on the boulder that has a direction vertically downward.

In terms of alpha and w, what is the component of the weight of the boulder in the direction parallel to the surface of the hill?

Homework Equations





The Attempt at a Solution



I put w/sin(alpha) but this is wrong. As you can see I made the component parallel to the slope of the hill x so that means that sin(alpha)=w/x...solve for x and I get x=w/sin(alpha).

Apparently this is totally wrong.

I attached the diagram to the problem. Thanks for the help
 

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  • #2
You might want to re-evaluate the geometry of the situation. See the attached diagram.
 

Attachments

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  • #3
Ah okay thanks I would have never thought of that. How do we know that new angle is alpha? Is that common knowledge or a basic geometry fact? This problem was weird and hard for me because it is from chapter 1 of my book which covers models, measurements, and vectors. I read the whole chapter and it didn't discuss the concept of force at all. Thanks again.
 
  • #4
maff is tuff said:
Ah okay thanks I would have never thought of that. How do we know that new angle is alpha? Is that common knowledge or a basic geometry fact? This problem was weird and hard for me because it is from chapter 1 of my book which covers models, measurements, and vectors. I read the whole chapter and it didn't discuss the concept of force at all. Thanks again.

The fact that the "new" angle shown in gneill's diagram is alpha is so fundamentally obvious from the basics of geometry that the fact that you even have to ask leads me to think that you do not have the basic math background that is expected before you get to trig. What grade are you in? What math have you already taken?
 
  • #5
phinds said:
The fact that the "new" angle shown in gneill's diagram is alpha is so fundamentally obvious from the basics of geometry

It's obvious to me that it's the same angle just by inspection, but how would you prove it?

edit: Don't worry, just did it.
 
Last edited:
  • #6
It looks obvious now that it is the same angle. If you tilt everything 90 degrees then the perpendicular-to-the-slant line becomes parallel to the slant and the straight down line becomes parallel to the ground. Sorry for the dumb question; I'll try to think things over more before I post.
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles and the measurement of their sides and angles.

2. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent, which are defined as the ratios of the sides of a right triangle.

3. How is trigonometry used in physics?

Trigonometry is used in physics to calculate unknown angles and distances in a variety of physical situations, such as projectile motion and forces acting on objects at an angle.

4. What is the difference between trigonometry and geometry?

Trigonometry focuses on the relationships and properties of triangles, while geometry deals with the properties of shapes and figures in general.

5. How can I apply trigonometry in real life?

Trigonometry has many practical applications in fields such as engineering, architecture, navigation, and astronomy. It can be used to solve problems involving angles, distances, and heights in real-world scenarios.

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