Projectile-car system and momentum

[Kolika28]

Homework Statement

I don't understand what I'm doing wrong. When it comes to this problem

Relevant Equations

Moment=velocity*mass

I have done question 1. But I'm struggling with the other one. So since the only thing I know about the rocket is the mass and the velocity, I guess I have to use momentum to solve this problem. From the first question, I found out that the x-velocity of the projectile is $v_x=5 m/s*cos(30)=4,33 m/s$. I assume that the momentum of the projectile and the car is 0 before launching the projectile. So $0=m_{projectile}*v_{projectile}+m_{car}*v_{car}=4,33m/s*1kg-5kg*v_{car}$. Then I get that $v_{car}=0,866 m/s$. But in the solution I'm given the answer should be $11,5 m/s$. What I'm a doing wrong?

 

[Halc]

Yes, momentum is the way to solve it, and I got the same answer you did.
No idea where the book's answer is coming from. It has the more massive car moving faster than the projectile it fired, which violates horizontal momentum conservation.

11,5 is how many seconds it takes that car to move 10 meters, if that's any help.

 

[Kolika28]

Yes, momentum is the way to solve it, and I got the same answer you did.
No idea where the book's answer is coming from. It has the more massive car moving faster than the projectile it fired, which violates horizontal momentum conservation.

Thank you so much for the answer. I don't know either what's wrong with the solution. But it is good to know that I'm right at least. Thank you again!