The Trajectory of a Charge in an Electric Field

[evilempire]

My question reads as such:

An charge with mass m and charge q is emitted from the origin, (x=0,y=0). A large, flat screen is located at x=L. There is a target on the screen at y position yh, where yh>0. In this problem, you will examine two different ways that the charge might hit the target. Ignore gravity in this problem.

Assume that the charge is emitted with velocity v0 in the positive x direction. Between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. What should the magnitude E of the electric field be if the charge is to hit the target on the screen?

So far, I've managed to resolve the two equations of motion, for the X and Y directions, and t final. They are as such:

x(t)=v0*t
y(t)=(1/2)*(q*E/m)*t^2
tfinal= L/v0

My problem is synthesizing these into one equation that solves for E. Any help would be greatly appreciated.

 

[dextercioby]

Put the condition that the particle hits the target
$$x(t*)=L$$
$$y(t*)=y_{h}$$

Daniel.

 

[evilempire]

Put the condition that the particle hits the target
$$x(t*)=L$$
$$y(t*)=y_{h}$$

Daniel.

Oops, my bad. I actually had that figured out as well. Thanks for the help, though. :)

EDIT: What I don't understand is what parts go into the E equation. We just got introduced to this concept a few days ago and I am having difficulty translating the concept of kinematics to that of an electrical field E, which is what seems to need to be done here.

 

[evilempire]

Is there something I am missing?

 

[dextercioby]

Well,yeah...

$$L=v_{0}t$$ (1)

$$y_{h}=\frac{qE}{2m} t^{2}$$ (2)

Express "t" from (1) and plug it into (2) and extract "E".

Daniel.

 

[evilempire]

Well,yeah...

$$L=v_{0}t$$ (1)

$$y_{h}=\frac{qE}{2m} t^{2}$$ (2)

Express "t" from (1) and plug it into (2) and extract "E".

Daniel.

Ah. I understand now. The 'm' was what was throwing me off. Thank you very much for the help.

 

[evilempire]

I have another problem actually that I need a bit of guidance on. I will detail it here, rather than waste another threadspace:

There are three spheres: red, yellow, and blue. Blue is on the origin, red at d1,0, and yellow at (d2cos(theta),-d2sin(theta))

Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge Qred on the red sphere.

I have the two force components necessary to solve the equation figured out. Once again, my trouble is putting them together to solve for charge Q, something that has not been covered in my course yet.

Here are my two force equations:

Fx(yellow)=k*2*q^2*cos(theta)/(d_2)^2
Fx(red)=-k*q_red*q/d_1^2

so, q_red=... is what I am trying to find.