Calculating X componet of Velocity in collision

[connie5828]

Homework Statement

An object of mass 21 kg going to the right with
a speed of 27 m ⁄ s collides with a(n) 12 kg object at rest.
After collision the 21 kg object moves with a speed of 11 m ⁄ s
making an angle of 20 degree with the horizontal-right.
Calculate the x-component of the velocity of the 12 kg
object after collision.

Homework Equations

m₁v_lix+m₂V_2ix=m₁v_lfx+m₂v_2fx
I am not understanding if this is the right equation. My textbook is not giving enough information

The Attempt at a Solution

An attempt was made and the # wasn't even in the ballpark of the multiple choice answers.

 

[tiny-tim]

hi connie!

that is the correct equation …

show us your full calculations, and then we'll see what went wrong, and we'll know how to help

 

[connie5828]

Let me start here:
M₁=21
v_lix= 27* cos 0^o
m₂=12
v_2ix=0*cos0
v_lfx= 11*cos20
v_2fx=??

Are these correct before I go further? Thanks so much for the help.

 

[tiny-tim]

hi connie!

(just got up :zzz: …)

Let me start here:
M₁=21
v_lix= 27* cos 0^o
m₂=12
v_2ix=0*cos0
v_lfx= 11*cos20
v_2fx=??

Are these correct before I go further? Thanks so much for the help.

looks ok so far, but it would be better and quicker if you would show your whole calculations in one go (you only have to copy what you've already done), rather than a bit at a time

 

[rwisz]

As a scientist, it is important to understand the equations and concepts involved in solving a problem. In this case, it appears that the equation provided is the conservation of momentum equation, which is correct. However, it is important to note that this equation only applies in scenarios where there are no external forces acting on the system. In the given problem, it is not specified if there are any external forces, so it is important to clarify this before attempting a solution.

Assuming there are no external forces, the conservation of momentum equation can be used to solve for the x-component of the velocity of the 12 kg object after the collision. The equation should be set up as follows:

m1v1i cosθ1 + m2v2i cosθ2 = m1v1f cosθ1 + m2v2f cosθ2

Where m1 and m2 are the masses of the two objects, v1i and v2i are the initial velocities of the two objects, v1f and v2f are the final velocities of the two objects, and θ1 and θ2 are the angles at which the objects move after the collision.

In this case, the equation would look like this:

(21 kg)(27 m/s) cos(0°) + (12 kg)(0 m/s) cos(0°) = (21 kg)(11 m/s) cos(20°) + (12 kg)(vx) cos(0°)

Solving for vx, the x-component of the velocity of the 12 kg object after the collision, we get:

vx = [(21 kg)(27 m/s) cos(0°) + (12 kg)(0 m/s) cos(0°) - (21 kg)(11 m/s) cos(20°)] / (12 kg)

vx = 9.6 m/s

This value should be in the ballpark of the multiple choice answers, so it is possible that there was an error in the attempt at a solution. It is important to double check calculations and units to ensure accuracy.