Physics illiterate Finding Magnitude and Direction given displacement vectors

In summary, the problem involves a grasshopper making four jumps with displacement vectors of (1) 24.0 cm, due west; (2) 23.0 cm, 31.0 degrees south of west; (3) 23.0 cm, 33.0 degrees south of east; and (4) 34.0 cm, 46.0 degrees north of east. The goal is to find the magnitude and direction of the resultant displacement, expressed with respect to due west. To solve the problem, one must use trigonometry and draw a visual representation of the vectors to help conceptualize the solution.
  • #1
jdp123
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0

Homework Statement



A grasshopper makes four jumps. The displacement vectors are (1) 24.0 cm, due west; (2) 23.0 cm, 31.0 degrees south of west; (3) 23.0 cm, 33.0 degrees south of east; and (4) 34.0 cm, 46.0 degrees north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction with respect to due west. (Note: Use the convention that an angle south of west is positive, and an angle north of west is negative.)

Homework Equations


The Attempt at a Solution



I do know that you have to solve using components, but the assignment that I'm doing is online and every answer that I've entered so far has been wrong...so clearly I'm doing something wrong. If anyone could help, with workings, I would be SO appreciative!
 
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  • #2
Have you drawn a picture to help you visualize the problem? It's nothing more than a trigonometry problem if you know conceptually what you have to do.
 
  • #3
I have! That's a reason why I find physics so difficult. I feel that even when I do draw the vectors, I still find it extremely hard to visualize what it is that I'm looking for.
 

1. What is a displacement vector in physics?

A displacement vector in physics is a mathematical representation of the distance and direction of an object's movement from its starting point to its ending point. It is typically represented by an arrow, with the length of the arrow representing the magnitude of the displacement and the direction of the arrow indicating the direction of movement.

2. How do you find the magnitude of a displacement vector?

The magnitude of a displacement vector can be found using the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of the vector's components. In simpler terms, you square the x-component of the vector, square the y-component, add them together, and then take the square root of that sum.

3. How is direction represented in a displacement vector?

Direction is represented in a displacement vector by the angle that the vector makes with the positive x-axis. This angle can be measured using a protractor or calculated using trigonometric functions.

4. Can a displacement vector have a negative magnitude?

Yes, a displacement vector can have a negative magnitude. This simply indicates that the object has moved in the opposite direction of the vector's direction. For example, a displacement vector with a magnitude of -5 meters would mean that the object has moved 5 meters in the opposite direction of the vector's direction.

5. How do you find the direction of a displacement vector?

The direction of a displacement vector can be found using trigonometric functions, specifically the tangent function. By taking the inverse tangent of the y-component divided by the x-component, you can find the angle that the vector makes with the positive x-axis.

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