Conservation of Momentum and Relative Velocity

In summary, the student has a resultant velocity of 0.25 m/s when standing on the surfboard and then walking with a velocity of 1.9 m/s.
  • #1
whoareyou
162
2

Homework Statement



A 55kg 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. Determine the resultant velocity of the surfboard, relative to the water. Neglect Friction.
Answer: 0.25 m/s[E]

Homework Equations



Conservation of momentum (P = P')

The Attempt at a Solution



I plugged in the values given (relative to the water) into the equation, but I'm not getting the right answer ?

vGoBS.jpg


ms = mass of student
mb = mass of board
vs = 2.0m/s
vb = 2.0m/s
vs' = 1.9m/s + 2.0m/s
vb' = ?
 
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  • #2
whoareyou said:

Homework Statement



A 55kg 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. Determine the resultant velocity of the surfboard, relative to the water. Neglect Friction.
Answer: 0.25 m/s[E]

Homework Equations



Conservation of momentum (P = P')

The Attempt at a Solution



I plugged in the values given (relative to the water) into the equation, but I'm not getting the right answer ?

vGoBS.jpg
Your top equation is correct. But before solving for v'B, you'll need to correct a mistake.

(The bottom equation is technically correct too, but it's too early to solve for v'B. Solving for it at this point doesn't make the problem easier.)
ms = mass of student
mb = mass of board
vs = 2.0m/s
vb = 2.0m/s
vs' = 1.9m/s + 2.0m/s
vb' = ?

The error is your
vs' = 1.9m/s + 2.0m/s​
equation. That's not right.

The way you've expressed the equation, the board maintains its 2.0 m/s velocity even after the surfer starts walking. But that's not right. The board has a different velocity when the surfer is walking. You need to replace that 2.0 m/s with with the new velocity of the board. :wink: (Hint: the new velocity of the board is a variable that you haven't solved for just yet.)
 
  • #3
But isn't the new velocity of the board what we're trying to solve for?
 
  • #4
whoareyou said:
But isn't the new velocity of the board what we're trying to solve for?
Yes, that's right! :approve:

(Another hint: you have a little more algebra to do. :wink:)
 
  • #5
So then if 2.0m/s is not the final velocity of the surfboard, then it would be 1.9m/s + vb' ?
 
  • #6
whoareyou said:
So then if 2.0m/s is not the final velocity of the surfboard, then it would be 1.9m/s + vb' ?
No not quite.

But the student is walking at 1.9 m/s relative to the board.

So that means the velocity of the student is v's = 1.9 m/s + v'b.

[Edit: I was calling the student a 'surfer'. Changed it back to 'student' in this post.]
 
  • #7
It works out! Thanks a lot! :D

o9zAl.jpg
 
  • #8
There ya' go. :approve:
 

1. What is conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This means that momentum cannot be created or destroyed, only transferred between objects.

2. How does the mass and velocity of objects affect conservation of momentum?

According to the law of conservation of momentum, the total momentum of a system remains constant. This means that if one object has a larger mass or velocity, the other object must have a smaller mass or velocity in order to maintain the same total momentum.

3. What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the objects involved bounce off each other without any loss of energy. In an inelastic collision, momentum is conserved but some kinetic energy is lost. This typically occurs when objects stick together after colliding.

4. How do you calculate relative velocity?

Relative velocity is the measurement of the speed and direction of an object in relation to another object. To calculate it, you must first determine the velocity of each object and then subtract them to find the difference in speed and direction.

5. Why is conservation of momentum important in physics?

Conservation of momentum is an important concept in physics because it allows us to predict the outcomes of collisions and interactions between objects. It also helps us understand the behavior of objects in motion and how energy is transferred between them.

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