Final answer:
The electron must be placed approximately 2.94 meters away from the point charge along the y-axis for the electric force to be exactly opposite to its weight.
Step-by-step explanation:
To determine where an electron must be placed so that the electric force acting on it is exactly opposite to its weight, we equate the magnitude of the electrical force to the gravitational force acting on the electron.
The electrical force Felec is given by Coulomb's Law, Felec = k |q1q2| / r2, where k is the Coulomb's constant (8.99 × 109 Nm2/C2), q1 is the charge of the fixed particle, q2 is the charge of the electron (-1.60 × 10-19 C), and r is the distance between the charges.
The gravitational force Fgrav on the electron is meg, where me is the mass of the electron (9.11 × 10-31 kg) and g is the acceleration due to gravity (9.8 m/s2).
By setting Felec equal to Fgrav, and solving for r, we can find the position where the electron should be placed. The vertical position along the y-axis should be such that r is the distance from the origin to the electron to balance the forces.