Need a bit of help with j-hat and i-hat in a collision

In summary, the conversation is about finding the velocity of the center of mass of a system with two 3-kg masses, each with their own velocity vector including i-hat and j-hat components. The formula for calculating the velocity of the center of mass is mentioned, but the use of i-hat and j-hat is causing confusion. The speaker suggests treating them as separate problems and then combining them into a momentum vector.
  • #1
jperez94
4
0
Hey there, I'm lost with this one:

Two 3-kg masses have velocities v(1)= 2m/s i-hat plus 3m/s j-hat and v(2)= 4m/s i-hat minus 6m/s j-hat. Find the velocity of the center of mass of the system.


Now, I know how to go about calculating the velocity of the center of mass (v(cm)= m(1)V(1)+m(2)V(2)/m(1)+m(2)

The thing that throws me off is the j-hats and i-hats. How do I come out with a vector number? I thought of the pothagarem(sp?) therom, but decided that couldn't work. Any ideas? Thanks.
 
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  • #2
u mean pythagoras Theorem , it should work
 
  • #3
Treat "i-hat" and "j-hat" as two separate problems. Then put them back together into the "momentum vector" with i and j components.
 

FAQ: Need a bit of help with j-hat and i-hat in a collision

1. What is j-hat and i-hat in a collision?

J-hat and i-hat are unit vectors that represent the directions of motion in a two-dimensional collision. J-hat represents the direction of motion along the y-axis, while i-hat represents the direction of motion along the x-axis.

2. Why are j-hat and i-hat important in a collision?

J-hat and i-hat help us analyze the components of velocity and momentum in a collision. By breaking down the vectors into their respective directions, we can better understand the behavior of the objects involved in the collision.

3. How are j-hat and i-hat calculated?

J-hat and i-hat are calculated by dividing the velocity vectors along the y-axis and x-axis, respectively, by their magnitudes. This gives us unit vectors that represent the direction of motion in each direction.

4. Can j-hat and i-hat be negative?

Yes, j-hat and i-hat can be negative if the motion in their respective directions is in the opposite direction of the positive axis. This can happen if the objects involved in the collision have a negative velocity in that direction.

5. How do j-hat and i-hat affect the outcome of a collision?

J-hat and i-hat play a crucial role in determining the final velocities and momenta of the objects involved in a collision. By analyzing the vectors in each direction, we can calculate the changes in velocity and momentum and predict the outcome of the collision.

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