A 4.75 mass was dropped from a certain height and achieved a maximum velocity of 7.68 m/s just before striking the ground. Determine the height from which the mass was dropped. Ignore air drag.

To determine the height from which the mass was dropped, we can use the principles of kinematics.

First, let's determine the final velocity just before striking the ground (v_final). We know that the maximum velocity achieved is 7.68 m/s.

Next, we need to determine the acceleration due to gravity (g). We know that on Earth, the acceleration due to gravity is approximately 9.8 m/s^2.

Using the kinematic equation:

v_final^2 = v_initial^2 + 2 * a * d

where:
- v_final is the final velocity (7.68 m/s)
- v_initial is the initial velocity (0 m/s, since the object is dropped)
- a is the acceleration (in this case, the acceleration due to gravity, -9.8 m/s^2 since it acts in the opposite direction of the motion)
- d is the displacement or height from which the object is dropped (unknown)

Substitute the values into the equation:

(7.68 m/s)^2 = 0^2 + 2 * (-9.8 m/s^2) * d

Simplifying the equation:

59.14 m^2/s^2 = -19.6 m/s^2 * d

Divide both sides of the equation by -19.6 m/s^2:

d = 59.14 m^2/s^2 / -19.6 m/s^2

The acceleration due to gravity is negative because it acts in the opposite direction of the motion (downward). Note that it cancels out in the calculations, so we can ignore the negative sign for now.

d = -3.01 m^2/s^2

Therefore, the height from which the mass was dropped is approximately 3.01 meters.