Power Lift
1. The problem asks for the power required to lift a mass of 30.0 kg to a height of 10.0 m in 5.00 s.
2. Power is the rate at which work is done, so we first calculate the work done in lifting the object. Work done against gravity is equal to the gravitational potential energy gained: $$W = mgh$$ where $m = 30.0$ kg, $g = 9.8\ \text{m/s}^2$, and $h = 10.0$ m.
3. Calculate the work: $$W = 30.0 \times 9.8 \times 10.0 = 2940\ \text{J}$$
4. Power is work done over time: $$P = \frac{W}{t}$$ where $t = 5.00$ s.
5. Calculate power: $$P = \frac{2940}{5.00} = 588\ \text{W}$$
Final answer: The power required is $$588\ \text{watts}$$.