Final answer:
The horizontal component of an electron's velocity remains constant when no horizontal force acts on it, while the vertical displacement can be calculated using motion equations with the known force, mass, and horizontal travel distance.
Step-by-step explanation:
The question concerns an electron with a horizontal initial speed of 8.0 x 10⁶ m/s entering a region with a constant vertical force of 6.4 x 10⁽¹⁷ N. The horizontal component of the velocity remains unchanged because no force is acting on the electron in the horizontal direction according to Newton's first law of motion. Calculation of the vertical displacement involves using the equations of motion under constant acceleration caused by the vertical force.
To find the vertical displacement, we'll use the formula s = ut + 0.5at², where u is the initial vertical velocity (which is zero), a is the vertical acceleration, and t is the time the electron is in the force field. The vertical acceleration a can be calculated using Newton's second law, F = ma, where F is the vertical force and m is the mass of the electron.
With the given values, the vertical acceleration is a = F/m = (6.4 x 10⁽¹⁷ N) / (9.11 x 10⁽³¹ kg). The time t can be found by the horizontal motion, as velocity v = distance/time, giving t = distance/v = (0.25 m) / (8.0 x 10⁶ m/s). With a and t calculated, we can find the vertical displacement s.