Conservation of momentum: Student walking on surfboard find resultant velocity

[n3w ton]

Homework Statement

A 55 kg student stands on a 4.6 kg surfboard moving at 2.0 m/s [E]. The student then walks with a velocity of 1.9 m/s [E] relative to the surfboard, relative to the water. Neglect Friction.

Answer: 0.25 m/s[E]

Homework Equations

m₁v_i1 + m₂v_i2 = m₁v_f1 + m₂v_f2

The Attempt at a Solution

m₁= 55kg
m₂= 4.6kg
v_i1= ?
v_i2= ?
v_f1= ?
v_f2= ?

How do I solve this? Please help me set up variables. Please and Thank you!

 

[HallsofIvy]

Solve what? You haven't stated a problem. You titled this "find resultant velocity", but resultant velocity of what? The student or the surfboard?

You need to use "conservation of momentum". The initial momentum of the "student-surfboard" system is 0 and so remains 0. In particular, the center of mass of the system will not move. Where is the center of mass initially? How does the student's center of mass move relative to that? How does the surfboard's center of mass move?

 

[e^(i Pi)+1=0]

He wasn't clear, but he's trying to solve for the final velocity of the surf board, because that's the only variable that's not given.

On the initial side of the equation, you have the student and surfboard moving together, so their velocity will be the same and their mass will be added. Using basic algebra, this turns m1vi1 + m2vi2 into vi(m1+m2).

^edit: surely the initial momentum isn't 0 except if it were measured by the student himself, but clearly this is a reference frame outside the system since the system's initial velocity is given as 2 m/s.