What Are the Final Velocities After a Two-Dimensional Collision?

[hdo]

problem:
before - 1st object: m=6kg, v=3m/s
2nd object: m=6kg, v=0m/s
after - 1st object move off in a direction 40 degree to the left of its original path
2nd move to the right of the first's original path
find the speech of each object after the collision
equations:
x-direction: m1v1ix + m2v2ix = m1v1fx + m2v2fx
y-direction: m1v1iy + m2v2iy = m1v1fy + m2v2fy

 

[tiny-tim]

Welcome to PF!

Hi hdo! Welcome to PF!:

(try using the X₂ tag just above the Reply box )

… 2nd move to the right of the first's original path

Do you mean at 90º?

ok, those are the correct equations … now put the numbers in …

what do you get? ​

(btw, all the masses are the same, 6 kg, so you can leave them all out! )

 

[astrokreng]

Based on the given information, it appears that the two objects have collided in a two-dimensional scenario. This means that the objects have both a horizontal and vertical component to their motion. To determine the final velocities of each object after the collision, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant before and after a collision.

Using the equations provided, we can set up a system of equations to solve for the final velocities. In the x-direction, we have:

m1v1ix + m2v2ix = m1v1fx + m2v2fx
6kg * 3m/s + 6kg * 0m/s = m1v1fx + 6kg * v2fx

Solving for the final velocity of the first object, we get:

m1v1fx = 6kg * 3m/s + 6kg * 0m/s - 6kg * v2fx
m1v1fx = 18kgm/s - 6kgv2fx
v1fx = (18kgm/s - 6kgv2fx) / 6kg
v1fx = 3m/s - v2fx

Similarly, in the y-direction, we have:

m1v1iy + m2v2iy = m1v1fy + m2v2fy
0kg * 3m/s + 6kg * 0m/s = m1v1fy + 6kg * v2fy

Solving for the final velocity of the first object, we get:

m1v1fy = 0kg * 3m/s + 6kg * 0m/s - 6kg * v2fy
m1v1fy = 0kgm/s - 6kgv2fy
v1fy = (0kgm/s - 6kgv2fy) / 6kg
v1fy = -v2fy

Therefore, the final velocities of the two objects are:

Object 1: v1fx = 3m/s - v2fx, v1fy = -v2fy
Object 2: v2fx = v2fx, v2fy = 0m/s

To find the direction of the final velocities, we can use the trigonometric relationship between the angle of motion and