1. **Problem:** Calculate the kinetic energy (KE) of 1200 kg of water moving at 2.5 m/s. 2. **Formula:** Kinetic energy is given by $$KE = \frac{1}{2} m v^2$$ where $m$ is mass and $v$ is velocity. 3. **Calculation:** $$KE = \frac{1}{2} \times 1200 \times (2.5)^2 = 600 \times 6.25 = 3750$$ Joules 4. **Answer:** The kinetic energy of the moving water is 3750 Joules. 1. **Problem:** Calculate the kinetic energy of 250 kg of air moving at 18 m/s. 2. **Formula:** Same as above. 3. **Calculation:** $$KE = \frac{1}{2} \times 250 \times (18)^2 = 125 \times 324 = 40500$$ Joules 4. **Answer:** The kinetic energy of the air parcel is 40500 Joules. 1. **Problem:** Calculate the kinetic energy of 50 kg debris moving at 3.2 m/s. 2. **Formula:** Same as above. 3. **Calculation:** $$KE = \frac{1}{2} \times 50 \times (3.2)^2 = 25 \times 10.24 = 256$$ Joules 4. **Answer:** The kinetic energy of the debris is 256 Joules. 1. **Problem:** A 15 kg bike is raised 0.8 m high and then moves downhill at 5 m/s. Find potential energy (PE) on the stand and kinetic energy (KE) while moving. 2. **Formulas:** - Potential energy: $$PE = m g h$$ where $g = 9.8 \text{ m/s}^2$ (acceleration due to gravity) - Kinetic energy: $$KE = \frac{1}{2} m v^2$$ 3. **Calculations:** - PE: $$PE = 15 \times 9.8 \times 0.8 = 15 \times 7.84 = 117.6$$ Joules - KE: $$KE = \frac{1}{2} \times 15 \times (5)^2 = 7.5 \times 25 = 187.5$$ Joules 4. **Answers:** - Potential energy on the stand is 117.6 Joules. - Kinetic energy while moving is 187.5 Joules.