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:** For a 15 kg bike raised 0.8 m high and moving at 5 m/s, find: a) Potential energy (PE) on the stand b) Kinetic energy (KE) while moving 2. **Formulas:** - Potential energy: $$PE = m g h$$ where $g = 9.8$ m/s² (gravity), $h$ is height. - Kinetic energy: $$KE = \frac{1}{2} m v^2$$ 3. **Calculations:** - a) $$PE = 15 \times 9.8 \times 0.8 = 15 \times 7.84 = 117.6$$ Joules - b) $$KE = \frac{1}{2} \times 15 \times (5)^2 = 7.5 \times 25 = 187.5$$ Joules 4. **Answers:** - a) Potential energy on the stand is 117.6 Joules. - b) Kinetic energy while moving is 187.5 Joules.