Answer:
The z-component of the force is
Explanation:
From the question we are told that
The charge on the particle is
The magnitude of the magnetic field is 
The velocity of the particle toward the x-direction is 
The velocity of the particle toward the y-direction is

The velocity of the particle toward the z-direction is

Generally the force on this particle is mathematically represented as

So we have

substituting values
So the z-component of the force is
Note : The cross-multiplication template of unit vectors is shown on the first uploaded image ( From Wikibooks ).
Answer: The average speed is 27,24 mph (exactly 1008/37 mph)
Explanation:
This is solved using a three rule: We know the speeds and the distances, what we can obtain from it is the time used. It is done like this:
1h--->18mi
X ---->20 mi, then X=20mi*1h/18mi= 10/9 h=1,111 h
1h--->56mi
X ---->20 mi, then X=20mi*1h/56mi= 5/14 h=0,35714 h
Then the average speed is calculated by taking into account that it was traveled 40mi and the time used was 185/126 h=1,468 h and since speed is distance over time we get the answer. Average speed= 40mi/(185/126 h)=1008/37 mph=27,24 mph.
I haven't, but I'm sure @Porshia has!
The force applied to the lever is 400 N, because the force applied by the lever (800 N) divided by the mechanical advantage of the lever (4) equals
400 N.
(800/4) = 200