A motor of 200 H.P. moves with a uniform speed of 72 km/h. The forward thrust applied by the engine on the car is

Options

A. 7460N
B. 3730N
C. 3550N
D. none of these

Answer

To find the forward thrust applied by the engine on the car, we can follow these steps:

### Step 1: Convert Horsepower to Watts
The power of the motor is given as 200 horsepower (H.P.). We know that 1 horsepower is equal to 746 watts. Therefore, we can convert the power from horsepower to watts:

\[ \text{Power (P)} = 200 \, \text{H.P.} \times 746 \, \text{W/H.P.} = 149200 \, \text{W} \]

### Step 2: Convert Speed from km/h to m/s
The speed of the car is given as 72 km/h. We need to convert this speed into meters per second (m/s). The conversion factor is:

\[ 1 \, \text{km/h} = \frac{1}{3.6} \, \text{m/s} \]

Thus,

\[ \text{Speed (v)} = 72 \, \text{km/h} \times \frac{1}{3.6} \approx 20 \, \text{m/s} \]

### Step 3: Use the Power-Force Relation
The relationship between power, force, and velocity is given by the formula:

\[ P = F \cdot v \]

Where:
- \( P \) is the power in watts,
- \( F \) is the force in newtons,
- \( v \) is the velocity in m/s.

We can rearrange this formula to solve for the force (thrust):

\[ F = \frac{P}{v} \]

### Step 4: Substitute the Values
Now we can substitute the values of power and speed into the formula:

\[ F = \frac{149200 \, \text{W}}{20 \, \text{m/s}} = 7460 \, \text{N} \]

### Conclusion
The forward thrust applied by the engine on the car is **7460 Newtons**.

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