1. Finding Electric Field (E):
- We use the formula E = (mg)/q, where m is the mass of the proton, g is the acceleration due to gravity, and q is the charge of the proton.
- Plugging in the values, we find E ≈ 1.02 × 10^5 N/C.
2. Finding Initial Vertical Velocity (vi):
- We use the formula vi = √(2aΔy), where a is the acceleration due to gravity (9.8 m/s^2) and Δy is the vertical displacement (given as 0.01 m).
- Substituting the values, we find vi ≈ 0.14 m/s.
3. Finding Time (t):
- We know that the time taken vertically (t) is the same as the time taken horizontally.
- So, t = (Δy)/vi.
- Substituting the values, we find t ≈ 0.071 s.
4. Finding Initial Horizontal Velocity (u):
- We use the formula u = (s)/t, where s is the horizontal displacement (given as 0.08 m) and t is the time.
- Substituting the values, we find u ≈ 1.13 m/s.
Therefore, the initial speed of the proton is approximately 1.13 m/s.
