Calculating Angle Between Vectors Using Cosine Law

  • Thread starter Thread starter Uira
  • Start date Start date
  • Tags Tags
    Angle Vectors
AI Thread Summary
To calculate the angle between two vectors using the cosine law, one must apply the formula c² = a² + b² - 2ab cos(C), where c is the resultant displacement and a and b are the magnitudes of the two displacements. The problem involves determining the angle that results in specific magnitudes for the resultant displacement, given two known displacements of 2.6 and 3.9. Understanding how to rearrange the cosine law formula to solve for the angle C is crucial for finding the solution. The discussion emphasizes the importance of learning the process rather than just obtaining the answer. Mastery of this concept will enhance one's ability to solve similar vector problems effectively.
Uira
Messages
1
Reaction score
0
Hello, I've been trying to solve this problem for hours now, but i keep getting it wrong. Been looking for examples but i don't seem to find one with a good explanation, so any help is appreciated.

The problem:

Consider two displacements, one of magnitude 2.6 and another of magnitude 3.9. What angle between the directions of these two displacements give a resultant displacement of magnitude a) 5.7m b)2.6m c)3.2

If anyone can please help me understand, thank you. Please, don't just post the answer, i want to learn how to solve it.
 
Physics news on Phys.org
This is referring to addition of the displacements.

You have a triangle, and know the lengths of the 3 sides. Find the angle/s.
 
A formula that will help is the cosine law. If a triangle has sides a, b, and c and C is the angle opposite side c, then c^2= a^2+ b^2- 2ab cos(C)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Vectors Directions: Where is this Resultant Vector Pointing?
Replies
14
Views
1K
Finding Vector Angle using cosine law
Replies
13
Views
2K
Needs clarity on this displacement vector diagram
Replies
3
Views
998
Vector Addition Question: find angle (A+B & A-B)
Replies
3
Views
1K
Is it possible to solve relative velocity problems without sine law?
Replies
25
Views
2K
Torque on a Circular Current Loop under a Misaligned Magnetic Field
Replies
1
Views
996
Calculate electric force using Coulomb's law (vector components are the struggle)
Replies
3
Views
1K
Finding the Magnitude and Angle of a Problem: Two Solutions
Replies
7
Views
2K
I finding resultants using sine/cosine law
Replies
9
Views
2K
Calculating Velocity Vector of Object in 2D Space
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top