# Finding z component of a unit vector

• Jonathan Lawler
In summary, the problem involves a 0.54 kg block of ice sliding on a slippery floor at 2.1 m/s. After being kicked perpendicularly, the block changes direction by 21 degrees. The student is struggling to find the z component of the unit vector and the block's momentum after the kick. They attempted to use the equation Pz = mvcos(90+21), but got an incorrect answer. To solve the problem, they should draw a diagram and use the information about the change in direction to label the sides of the triangle and determine the x and z components. Additionally, they should consider if the velocity in the x direction has changed and use this to find the magnitude of the average force applied
Jonathan Lawler

## Homework Statement

A 0.54 kg block of ice is sliding by you on a very slippery floor at 2.1 m/s. As it goes by, you give it a kick perpendicular to its path. Your foot is in contact with the ice block for 0.0034 seconds. The block eventually slides at an angle of 21 degrees from its original direction.

Found:
Unit vector :< .92, 0, Z >
(z is unknown)
x component: of block momentum = 1.134 kg m/s
magnitude of block momentum : 1.21 kg m/s

Need help with:
1. What is the unit vector in the direction of the block's momentum after the kick?
I am struggling to find the z component of the unit vector and of the block momentum after its kicked

2. What was the magnitude of the average force you applied to the block?

## Homework Equations

Pz = mvcos(90+21)

## The Attempt at a Solution

I tried finding z component of the unit vector by doing .54kg x 2.1 m/s x cos(90+21) and got -.4m/s but its wrong so I don't know what else to do. As a result I don't know how to get the z component of the block momentum or how to get magnitude of average force.

Jonathan Lawler said:
I tried finding z component of the unit vector by doing .54kg x 2.1 m/s x cos(90+21)
Did you draw a diagram? In a right angled triangle with the given acute angle, which sides represent the x and z components?

Also ask yourself has the velocity of the block in the x direction (assumed to be the original direction) changed? If so, why, and by how much? If not, why not? Use this information to help label the magnitude of the sides of the triangle in the diagram.

## 1. What is a unit vector?

A unit vector is a vector with a magnitude of 1, which means it has a length of 1 unit. It is often used to indicate direction and is commonly denoted by a hat symbol (^) above the vector symbol.

## 2. Why is it important to find the z component of a unit vector?

The z component of a unit vector is important because it tells us the direction of the vector in the z-axis. This is essential in three-dimensional space, where vectors can have components in the x, y, and z directions.

## 3. How do you find the z component of a unit vector?

To find the z component of a unit vector, you can use the formula z = cos(θ), where θ is the angle between the vector and the z-axis. Alternatively, you can use the dot product of the vector with the unit vector in the z-direction, which will give you the magnitude of the z component.

## 4. Can the z component of a unit vector be negative?

Yes, the z component of a unit vector can be negative. This indicates that the vector is pointing in the negative z-direction, which is opposite to the positive z-direction.

## 5. What is the difference between a unit vector and a regular vector?

A unit vector has a magnitude of 1, while a regular vector can have any magnitude. Unit vectors are used to indicate direction, while regular vectors can represent both magnitude and direction. Additionally, unit vectors are often written with a hat symbol above the vector symbol, while regular vectors do not have this notation.

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