What Speed Do Ice Skaters Reach After a Collision?

[sweedeljoseph]

Homework Statement

A 35 kg ice skater traveling at 12 m/s runs head-on into a 65 kg skater traveling straight forward at 4 m/s. At what speed do the ice skaters travel if they move (stuck) together after the collision?

Homework Equations

i put it below. i don't know if youre supposed to use something else. or if there's something eaiser.

The Attempt at a Solution

answer from the teacher is 1.6 m/s.

i tried this:
m₁*v₁+m₂*v₂=m₁'*v₁'+m₂'*v₂'
m₁*v₁+m₂*v₂=v'(m₁'+m₂')
v=(m₁*v₁+m₂*v₂)/(m₁'+m₂')
v=((35*12)+(65*4))/100
v=6.8

thats what i got. is it all wrong? i know the equation stuff isn't because that's from my teacher. but when i do the math its not the same. its supposed to be 1.6 m/s. am i missing a step?

thank you!
sweedeljoseph

 

[asleight]

Homework Statement

A 35 kg ice skater traveling at 12 m/s runs head-on into a 65 kg skater traveling straight forward at 4 m/s. At what speed do the ice skaters travel if they move (stuck) together after the collision?

Homework Equations

i put it below. i don't know if youre supposed to use something else. or if there's something eaiser.

The Attempt at a Solution

answer from the teacher is 1.6 m/s.

i tried this:
m₁*v₁+m₂*v₂=m₁'*v₁'+m₂'*v₂'
m₁*v₁+m₂*v₂=v'(m₁'+m₂')
v=(m₁*v₁+m₂*v₂)/(m₁'+m₂')
v=((35*12)+(65*4))/100
v=6.8
thats what i got. is it all wrong? i know the equation stuff isn't because that's from my teacher. but when i do the math its not the same. its supposed to be 1.6 m/s. am i missing a step?

The velocity of the second skater's not inputted correctly; reassess the system.

 

[Saladsamurai]

Keep in mind the skaters are skating "head on". What does that say about their directions relative to each other? So what does that say about the signs of the velocities?

Casey

Edit: Asleight is quick! Last three posts we have been typing at the same time!

 

[sweedeljoseph]

the velocity of the 2nd skater is in wrong? i don't see where its wrong. m1=35, v1=12, m2=65 and v2=4. m1+m2=100. that's what i plugged in isn't it?

would the skaters going head on make any difference? there's no difference in the distance they traveled since they are together.

 

[sweedeljoseph]

i got it! haha I am kind of slow. the velocity for the 2nd skater was supposed to be negative. i don't know why i guess because she's going backwards to the 1st guy. but i get it now.

thank you!
sweedeljoseph

 

[Saladsamurai]

i got it! haha I am kind of slow. the velocity for the 2nd skater was supposed to be negative. i don't know why i guess because she's going backwards to the 1st guy. but i get it now.

thank you!
sweedeljoseph

Yes! Velocity is a vector and thus has a direction associated with it. Clearly is skater 1 is moving to the right and you consider his velocity to be positive then a skater moving in the OPPOSITE direction must have a velocity that is negative!

You could have chosen the opposite signs for each and gotten the same number. Albeit you would have gotten a negative answer, but that only indicates that the skater is moving in the opposite direction of the one you assumed it was.

Casey