Eelectrons, like all forms of matter, fall under the influence of gravity. if a electron is projected horizontly with a speed of one-tenth speed of light, how far will it fall in traversing 1 meter of horizontal distance.

t=s/v=1/0.1•3•10⁸ =3.33•10⁻⁸ s.

y=gt²/2=9.8•(3.33•10⁻⁸)²/2=5.44•10⁻¹⁵ m

To determine how far an electron will fall in traversing 1 meter of horizontal distance, we need to consider the effects of gravity on the electron's motion.

Firstly, we can assume that the electron is projected horizontally, meaning its initial vertical velocity is zero. Since gravity only acts in the vertical direction, it will not directly influence the electron's horizontal motion.

However, as the electron moves horizontally, gravity will cause it to fall vertically due to acceleration. The acceleration due to gravity on Earth is approximately 9.8 meters per second squared (9.8 m/s²).

To find the vertical distance the electron will fall while moving horizontally, we can use the kinematic equation:

d = 0.5 * a * t²

where:
d is the vertical distance,
a is the acceleration, and
t is the time taken to traverse 1 meter horizontally.

To find the time, t, we can use the equation:

v = d / t

where:
v is the horizontal velocity,
d is the horizontal distance, and
t is the time taken.

Given that the horizontal velocity is one-tenth (1/10) the speed of light, which is approximately 3 x 10^8 meters per second (3e8 m/s), the horizontal velocity would be:

v = (1/10) * 3e8 m/s

Now, we can rearrange the equation for time to solve for t:

t = d / v

Substituting the given values of d = 1 meter and v = (1/10) * 3e8 m/s into the equation:

t = 1 meter / [(1/10) * 3e8 m/s]

Simplifying further:

t = 1 meter / (0.1 * 3e8 m/s)
t = 1 meter / (3e7 m/s)
t = 3.333e-8 seconds

Now that we have the time taken, we can substitute this value into the vertical distance equation:

d = 0.5 * a * t²

Substituting the known values:

d = 0.5 * 9.8 m/s² * (3.333e-8 seconds)²
d = 0.5 * 9.8 m/s² * 1.11e-15 seconds²
d ≈ 5.43e-16 meters

Therefore, the electron will fall approximately 5.43e-16 meters vertically while traversing 1 meter horizontally.