Wicked proton trajectory problem

[TechFlyer]

I have no idea what formulas I'm supposed to use here, or possibly how to use them... any help would be great...

Protons are projected with an initial speed vi = 9.73 103 m/s into a region where a uniform electric field E = (-720 j) N/C is present, as shown in Figure P23.49. The protons are to hit a target that lies at a horizontal distance of 1.27 mm from the point where the protons cross the plane and enter the electric field in Figure 23.49.

(a) Find the two projection angles that will result in a hit.
(smaller angle)
(larger angle)
(b) Find the total time of flight for each trajectory.
(for the smaller angle)
(for the larger angle)

 

[StatusX]

Well, it's easy to get the force on the proton, so from there just use f=ma to get the motion. You'll have to break it up into components, so f_x = ma_x, etc.

 

[wais]

Hi there,

It seems like you are facing a challenging problem with your proton trajectory. Don't worry, figuring out which formulas to use and how to apply them can be a bit overwhelming at times. Here are some steps you can follow to help you solve this problem:

1. Identify the given information: In this case, we know the initial speed of the protons (vi = 9.73 x 10^3 m/s), the electric field present (E = -720 j N/C), and the horizontal distance to the target (1.27 mm).

2. Understand the concept: To solve this problem, you will need to use the equations of motion for a charged particle in an electric field. These equations describe the trajectory of a charged particle in the presence of an electric field.

3. Identify the unknowns: The problem asks for the two projection angles that will result in a hit (smaller and larger angle) as well as the total time of flight for each trajectory.

4. Use the equations of motion: You can use the equations of motion to solve for the unknowns. The two equations you will need are:

- Horizontal displacement: x = vit + (1/2)at^2
- Vertical displacement: y = viyt + (1/2)gt^2

5. Solve for the unknowns: Plug in the given values and solve for the unknowns. For part (a), you will have to solve for the two projection angles. For part (b), you will need to solve for the total time of flight for each trajectory.

Remember to pay attention to the units and to use the correct signs for the electric field and the gravitational acceleration.

I hope this helps you get started on solving the problem. Don't hesitate to ask for clarification or additional help if needed. Keep practicing and you will become more confident in using formulas and solving problems. Good luck!