An unruly demonstrator lifts a stone of mass 200 g from the ground and throuws it at his opponent. At the time of projection, the stone is 150 cm above the grond and has a speed of 3.00 m/s. Calculate the work doe by the demonstrator during the process. If it takes one second for the demonstrator tolift teh stone and throw, what horsepower does he use?

Explanation

To solve the problem, we need to calculate the work done by the demonstrator while lifting and throwing the stone, and then convert that work into horsepower.

### Step 1: Identify the given data
- Mass of the stone (m) = 200 g = 0.2 kg (since 1 g = 0.001 kg)
- Height above the ground (h) = 150 cm = 1.5 m (since 1 cm = 0.01 m)
- Speed at the time of projection (v) = 3.00 m/s
- Acceleration due to gravity (g) = 10 m/s² (standard approximation)

### Step 2: Calculate the change in potential energy (PE)
The potential energy at the height is given by the formula:
\[ PE = m \cdot g \cdot h \]
Substituting the values:
\[ PE = 0.2 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 1.5 \, \text{m} = 3 \, \text{J} \]

### Step 3: Calculate the change in kinetic energy (KE)
The kinetic energy at the time of projection is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values:
\[ KE = \frac{1}{2} \cdot 0.2 \, \text{kg} \cdot (3.00 \, \text{m/s})^2 = \frac{1}{2} \cdot 0.2 \cdot 9 = 0.9 \, \text{J} \]

### Step 4: Calculate the total work done (W)
The total work done by the demonstrator is the sum of the change in potential energy and the change in kinetic energy:
\[ W = PE + KE = 3 \, \text{J} + 0.9 \, \text{J} = 3.9 \, \text{J} \]

### Step 5: Calculate the power in watts
Power (P) is defined as work done per unit time. Since the work is done in 1 second:
\[ P = \frac{W}{t} = \frac{3.9 \, \text{J}}{1 \, \text{s}} = 3.9 \, \text{W} \]

### Step 6: Convert power to horsepower
1 horsepower (hp) is equivalent to 746 watts. To convert watts to horsepower:
\[ \text{Horsepower} = \frac{P}{746} = \frac{3.9 \, \text{W}}{746} \approx 0.00522 \, \text{hp} \]

### Final Result
The work done by the demonstrator is **3.9 J**, and the power used is approximately **0.00522 hp**.

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