1. Potential Energy at the Starting Point

* The rock's potential energy (PE) at the top of the bridge is given by: PE = mgh, where:

* m = mass (10 kg)

* g = acceleration due to gravity (9.8 m/s²)

* h = height (50 m)

* PE = (10 kg)(9.8 m/s²)(50 m) = 4900 J (Joules)

2. Potential Energy at the Midway Point

* At the midway point, the height is half the original height: 50 m / 2 = 25 m.

* PE at the midway point = (10 kg)(9.8 m/s²)(25 m) = 2450 J

3. Conservation of Energy

* The total mechanical energy (PE + KE) of the rock remains constant throughout its fall (ignoring air resistance).

* Therefore, the kinetic energy (KE) at the midway point is the difference between the initial PE and the PE at the midway point.

* KE at midway point = Initial PE - PE at midway point = 4900 J - 2450 J = 2450 J

Answer: The kinetic energy of the rock at the midway point of its fall is 2450 Joules.