What is the speed of two objects after a perfectly inelastic collision?

[Agent M27]

Homework Statement

A 6 kg object moving with a speed of 9.9 m/s collides with a 19 kg object moving with a velocity of 7.2 m/s in a direction 24* from the initial direction of motion of the 6 kg object. What is speed of the two objects after the collision if they remain stuck together?

Homework Equations

P_x = m₁v_1icos$$\theta$$+m₂v_2icos$$\theta$$ = m₁v_1fcos$$\theta$$ + m₂v_2fcos$$\theta$$

P_y = m₁v_1isin$$\theta$$+m₂v_2isin$$\theta$$ = m₁v_1fsin$$\theta$$ + m₂v_2fsin$$\theta$$

The Attempt at a Solution

Edit I realized my original way was faulty in its logic.

So what I did was I began by finding the initial and final momenta components in both the x and y directions for the two particles. Being that they stick together their final velocity ought to be the same.

$$\Sigma$$P_xi = m₁v₁cos$$\theta$$ + m₂v₂cos$$\theta$$

=184.37302

$$\Sigma$$P_yi = m₁v₁sin$$\theta$$ + m₂v₂sin$$\theta$$

=55.641573

As I mentioned their final velocity should be equal since they are stuck together. Equating my initial momenta to my final momenta in the x direction I get the following:

V_f = $$\frac{(m1v1cos\theta + m2v2cos\theta}{(m1+m2)cos\theta}$$

=8.072856 m/s

When I checked it using the momenta of the y direction I come to a different value for the final velocity which doesn't make sense so I know I made a mistake somewhere... Thanks in advance.

Joe



Edit: I tried a new way, but

 

[Doc Al]

Looks good to me.

 

[Agent M27]

Thanks Doc Al, are you referring to the first way I solved the problem or referring to this edited version? The first way did not work, so that's why I tried a new method. Thanks for all your help in all of my posts.

Joe

 

[vela]

Actually, your first attempt was the correct solution. How do you know the answer you got is wrong?

 

[Doc Al]

Thanks Doc Al, are you referring to the first way I solved the problem or referring to this edited version? The first way did not work, so that's why I tried a new method.

I was referring to your original post, which looked fine to me. (I haven't looked at your revision.)

 

[Agent M27]

It is an online homework module, and this is not the first question that I have been correct about and it kicked back my answer as incorrect...Thanks for your assistance.

Joe

 

[vela]

Thought so. Could be you're entering too many significant figures.

 

[inky]

Thought so. Could be you're entering too many significant figures.

Do you know the direction (angle) after collision?

 

[Doc Al]

Do you know the direction (angle) after collision?

Why would that matter?

 

[inky]

Why would that matter?

I mean after collision, two objects stuck together. So velocities are the same but problem didn't mention direction is angle theta. I think angles are not the same before and after collision.

 

[Doc Al]

I mean after collision, two objects stuck together. So velocities are the same but problem didn't mention direction is angle theta. I think angles are not the same before and after collision.

True, but the direction of the final velocity doesn't matter for this problem. All they ask for is the speed.