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

Answer

To find the forward thrust applied by the engine on the car, we need to use the relationship between power, force, and velocity. Here’s a step-by-step solution:

### Step 1: Convert Horsepower to Watts
The power of the motor is given as 200 horsepower (H.P.). We need to convert this to watts (W) since the SI unit of power is watts.

1 H.P. = 746 W

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

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

To convert km/h to m/s, we use the conversion factor:
\[ 1 \, \text{km/h} = \frac{1}{3.6} \, \text{m/s} \]

Thus,
\[ V = 72 \, \text{km/h} \times \frac{1}{3.6} = 20 \, \text{m/s} \]

### Step 3: Use the Power Formula to Find Force
The relationship between power (P), force (F), and velocity (V) is given by the formula:
\[ P = F \times V \]

We can rearrange this to solve for force:
\[ F = \frac{P}{V} \]

### Step 4: Substitute the Values
Now we can substitute the values we calculated 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 N**.

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