Final answer:
To determine how far the proton travels before reaching its turning point, we need to consider the forces acting on the proton, including the electric field created by the positively charged plate. By calculating the force, acceleration, and using the equation for distance traveled, we can find the answer.
Step-by-step explanation:
To determine how far the proton travels before reaching its turning point, we need to consider the forces acting on the proton. The force due to the electric field created by the positively charged plate will slow down the proton. At the turning point, the force due to the electric field will be equal in magnitude but opposite in direction to the force due to the initial velocity of the proton.
Using the formula for the electric force, F = qE, where F is the force, q is the charge, and E is the electric field strength, we can find the force. The charge of a proton is 1.6 × 10^-19 C. The electric field strength can be calculated by dividing the charge density by the permittivity of free space.
Once we have the force, we can use Newton's second law, F = ma, to find the acceleration of the proton. Knowing the initial velocity and acceleration, we can find the time it takes for the proton to reach its turning point using the equation d = v0t + 0.5at^2. Here, d represents the distance traveled, v0 is the initial velocity, t is the time, and a is the acceleration.
By plugging in the values and solving the equation, we can determine how far the proton travels before reaching its turning point.