Finding z component of a unit vector

[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.

Thanks in advance for any help you can give!

 

[haruspex]

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?

 

[ZeusPerseus]

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.