Suppose a magnetic field of 50 microtesla is applied along south to north direction. With what velocity should an electron be projected towards the west so that the upward magnetic force may balance its weight? In which direction and with what speed should a proton be projected so that magnetic force may balance its weight? Take `g = 10 m//s^(2)`.

Explanation

To solve the problem, we need to find the velocity at which an electron should be projected towards the west so that the upward magnetic force balances its weight. We will also find the direction and speed at which a proton should be projected for the same condition.

### Step-by-Step Solution:

1. **Understand the Forces Involved:**
The magnetic force acting on a charged particle in a magnetic field is given by the formula:
\[
F = q(\mathbf{v} \times \mathbf{B})
...