Calculate the potential energy of the horse while standing on the hill

Here are the solutions to the physics problems:

Question 13: Calculate the potential energy of the horse while standing on the hill.

Step 1: Identify the given values. Mass of horse, $m = 100 \text{ kg}$ Height of hill, $h = 1.3 \text{ m}$ Acceleration due to gravity, $g = 10 m/s^2$

Step 2: Use the formula for potential energy ($PE$). $PE = mgh$

Step 3: Substitute the values and calculate. $PE = (100 kg) \times (10 m/s^2) \times (1.3 m)$ $PE = 1000 \times 1.3 \text{ J}$ $PE = 1300 \text{ J}$

The potential energy is $\boxed{1300 J}$.

Question 14: Calculate the kinetic energy used to run down the hill.

Step 1: Identify the given values. Mass of horse, $m = 100 \text{ kg}$ Speed of horse, $v = 5.0 \text{ m/s}$

Step 2: Use the formula for kinetic energy ($KE$). $KE = \frac{1}{2}mv^2$

Step 3: Substitute the values and calculate. $KE = \frac{1}{2} \times (100 kg) \times (5.0 m/s)^2$ $KE = \frac{1}{2} \times 100 kg \times 25 m^2/s^2$ $KE = 50 \times 25 \text{ J}$ $KE = 1250 \text{ J}$

The kinetic energy is $\boxed{1250 J}$.