# What is her velocity relative to the surface of the ice?

• Waveparticle
In summary, a 45-kg girl is standing on a 150-kg plank on a frictionless frozen lake. The girl starts walking at a constant velocity of 1.50m/s to the right relative to the plank. To solve this problem, we can use the concept of conservation of momentum, where the initial total momentum of the system is equal to the final total momentum. The initial velocities of the girl and the plank are both zero, and the only variable we need to solve for is the final velocity of the plank relative to the surface of the ice.
Waveparticle

## Homework Statement

A 45-Kg girl is standing on a 150-Kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50m/s to the right relative to the plank.
a)What is her velocity relative to the surface of the ice?
b)What is the velocity of the plank relative to the surface of the ice?

## Homework Equations

m1v1i+m2v2i=m1v1f+m2v2f

## The Attempt at a Solution

That place where it says "the attempt at a solution," is where you attempt to solve the problem---or where you explain what you're having trouble with so that we can help you accordingly.

The part I'm having trouble with is setting up the problem and plugging in the givens.

Start out thinking about it conceptually. You're on a plank, which has zero friction with the surface its lying on. As you start to walk in one direction, what happens to the plank?

The equation you gave is just conservation of momentum: the initial total momentum of the system has to be equal to the final total momentum of the system. Say that $$m_1$$ is the girl, and $$m_2$$ is the plank, what are their initial velocities? What else can you plug in for in the equation? What's left?

a) The girl's velocity relative to the surface of the ice can be calculated using the conservation of momentum equation, where m1 is the girl's mass and m2 is the plank's mass. Since the girl is walking at a constant velocity of 1.50m/s to the right relative to the plank, her initial velocity relative to the plank is also 1.50m/s to the right. This means that her final velocity relative to the plank is also 1.50m/s to the right. Therefore, her velocity relative to the surface of the ice is also 1.50m/s to the right.

b) The velocity of the plank relative to the surface of the ice can also be calculated using the conservation of momentum equation. Since the plank was originally at rest, its initial velocity relative to the surface of the ice is 0m/s. Using the same reasoning as in part a), the plank's final velocity relative to the surface of the ice is also 1.50m/s to the right. Therefore, the velocity of the plank relative to the surface of the ice is 1.50m/s to the right.

## 1. What is velocity?

Velocity is a measure of an object's speed and direction of motion. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. What is relative velocity?

Relative velocity is the measurement of the velocity of one object with respect to another object. It takes into account both objects' velocities and directions of motion.

## 3. What does "relative to the surface of the ice" mean?

This phrase indicates that the velocity is being measured in relation to the ice's surface, as opposed to another reference point. It is important to specify a reference point in order to accurately determine an object's velocity.

## 4. How is velocity relative to the surface of the ice calculated?

The velocity relative to the surface of the ice can be calculated by subtracting the ice's velocity from the object's velocity. This will give the object's velocity in relation to the ice's surface.

## 5. Why is it important to consider velocity relative to the surface of the ice?

It is important to consider the velocity relative to the surface of the ice because it can affect the motion and behavior of an object on the ice. For example, a skater's velocity relative to the surface of the ice will determine their speed and direction of movement on the ice.

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