Question about the solution to this elastic collision

[as2528]

Homework Statement

High-speed stroboscopic photographs show that the
head of a golf club of mass 200 g is traveling at 55.0 m/s
just before it strikes a 46.0-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just
after impact

Relevant Equations

1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2
m1v1i+mvv2i=m1v1f+m2v2f

I found that 1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2
=>0.5*200*55^2+0.5*46*0^2=0.5*40^2*200+0.5*46*0*vf^2=>vf=78.713 m/s.

The true answer is 65.2 m/s and is solved using m1v1i+mvv2i=m1v1f+m2v2f. Are these equations not interchangeable? Why can I not use the equation I used?

 

[kuruman]

The equations are not interchangeable. If they were, they would give the same answer. All collisions conserve momentum but not necessarily energy.

 

[as2528]

The equations are not interchangeable. If they were, they would give the same answer. All collisions conserve momentum but not necessarily energy.

I see. So the kinetic energy one works if energy is conserved? And should I always default to momentum?

 

[kuruman]

I see. So the kinetic energy one works if energy is conserved? And should I always default to momentum?

Yes, in a collision you default to momentum conservation. If you are told that the collision is perfectly elastic, then you can use energy conservation as well. Using both, usually involves questions where there are two unknowns.

 

[as2528]

Yes, in a collision you default to momentum conservation. If you are told that the collision is perfectly elastic, then you can use energy conservation as well. Using both, usually involves questions where there are two unknowns.

Thank you! This really cleared it up for me.