A horse exerts a pull a 500 N on a cart so that horse cart system moves with a uniform velocity of 36km/h what is the power developed by the horse in horse power ?

Options

A. 6.7HP
B. 7.8HP
C. 8.3HP
D. 10.5HP

Answer

To solve the problem of finding the power developed by the horse in horsepower, we can follow these steps:

### Step 1: Understand the given data
- The force exerted by the horse (F) = 500 N
- The velocity of the horse-cart system (v) = 36 km/h

### Step 2: Convert velocity from km/h to m/s
To convert the velocity from kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]
Thus, to convert 36 km/h to m/s:
\[ v = 36 \text{ km/h} \times \frac{1 \text{ m/s}}{3.6 \text{ km/h}} = 10 \text{ m/s} \]

### Step 3: Calculate the power in watts
Power (P) can be calculated using the formula:
\[ P = F \times v \]
Substituting the values we have:
\[ P = 500 \text{ N} \times 10 \text{ m/s} = 5000 \text{ W} \]

### Step 4: Convert power from watts to horsepower
To convert watts to horsepower, we use the conversion:
\[ 1 \text{ hp} = 746 \text{ W} \]
Thus, to convert 5000 W to horsepower:
\[ \text{Horsepower} = \frac{5000 \text{ W}}{746 \text{ W/hp}} \approx 6.7 \text{ hp} \]

### Final Answer:
The power developed by the horse is approximately **6.7 horsepower**.

---