Calculate the potential energy of the horse while standing on the hill
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
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, $g = 10 \text{ m/s}^2$
Step 2: Use the formula for potential energy ($PE$).
$$PE = mgh$$
Step 3: Substitute the values and calculate.
$$PE = (100 \text{ kg}) \times (10 \text{ m/s}^2) \times (1.3 \text{ m})$$
$$PE = 1000 \times 1.3 \text{ J}$$
$$PE = 1300 \text{ J}$$
The potential energy is $\boxed{\text{1300 J}}$.
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.
$$KE = \frac{1}{2} \times (100 \text{ kg}) \times (5.0 \text{ m/s})^2$$
$$KE = \frac{1}{2} \times 100 \text{ kg} \times 25 \text{ m}^2/\text{s}^2$$
$$KE = 50 \times 25 \text{ J}$$
$$KE = 1250 \text{ J}$$
The kinetic energy is $\boxed{\text{1250 J}}$.
