A. A uniform, upward-pointing electric field E of magnitude 3.00 10e3 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 4 cm and separation d = 2.00 cm. An electron is then shot between the plates from the left edge of the lower plate. The initial velocity v0 of the electron makes an angle theta=45 with the lower plate and has a magnitude of 6.93�10e6 m/s. Will the electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates ( m).

B.The next electron has an initial velocity which has the same angle theta=45 with the lower plate and has a magnitude of 5.83 10e6 m/s. Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates ( m).

I fixed the characters in the question please help

Ignore the plates for a second

PositionElectron=Vo*t+1/2 a t^2+ Positioninitial
now, you know a is F/m= Eq/m
PositionElectron= Vo*t+1/2 q/m E t^2+positioninitial

Vo and E are vectors.
Now breake Vo into horizontal and vertical components, and you have a position equation.

To see if they hit either plate, Just work with the vertical part of the equation.
find t when position=2, and find t when postion=0
if no solution,it does not hit plates.
Then, work with horizontal, find time when position horizontal is 4.
then use that time to find the vertical position.

Bobpursley thanks for the help I see that Eq/m=a is equal to F/m=a but what vaule do I use for m in this problem

What is the mass of an electron?

haha oh ok thanks

To determine if the electron will strike one of the plates or leave the space between the plates, we can use the equations of motion for a charged particle in a uniform electric field.

A. For the first electron with a velocity v0, we need to find its horizontal distance from the left edge (x) or the vertical position at which it leaves the space between the plates (y).

The electric field E provides a constant force on the electron, given by the equation:
F = qE,
where F is the force, q is the charge of the electron (1.6 x 10^-19 C), and E is the electric field.

The force acting on a charged particle in an electric field can also be expressed as:
F = ma,
where m is the mass of the electron (9.11 x 10^-31 kg) and a is its acceleration.

Since the electric force in the y-direction is balanced by the gravitational force, the electron experiences a constant acceleration in the x-direction only. Therefore, the force equation becomes:
F = ma_x,

We can relate the electric force to the acceleration in the x-direction using Newton's second law:
F = ma_x = qE.

Solving for a_x, we have:
a_x = (qE) / m.

Now, we can find the acceleration in the x-direction, using the given values of the charge of the electron, electric field, and the mass of the electron.

Once we have the acceleration in the x-direction, we can use the equations of motion to find the horizontal distance (x) traveled by the electron:
x = v_0x * t,
where v_0x is the initial velocity in the x-direction, and t is the time taken.

The time taken (t) can be found using the equation:
t = (v_0y - v_y) / a_y,
where v_0y is the initial vertical velocity, v_y is the vertical velocity at any given time, and a_y is the vertical acceleration.

If the electron strikes one of the plates, the horizontal distance (x) will be the total length (L) of the plates (4 cm). If it leaves the space between the plates, we need to find the vertical position (y) at which it exits.

B. The same method can be applied to determine if the second electron will strike one of the plates or leave the space between the plates. Just replace the initial velocity (v0) with the given value for the second electron (5.83 x 10^6 m/s).

By following these steps and performing the calculations, you can determine whether each electron will strike one of the plates or leave the space between the plates, along with the corresponding horizontal distance from the left edge or the vertical position at which it exits.