An automobile delivers 30.0 hp to its wheels when moving at a constant speed of \( 22.0 \mathrm{~m} / \mathrm{s} \). What is the resistance force on the automobile at this speed? ( \( \mathrm{hp}=746 \) watts) 1) 18600 N 2) 410000 N 3) 1020 N 4) 848 N 5) 763 N

To find the resistance force on the automobile, we need to convert horsepower to watts and then calculate the force using the relationship between power, force, and velocity. First, convert 30.0 hp to watts: \[ 30.0 \, \text{hp} = 30.0 \times 746 \, \text{W} = 22380 \, \text{W} \] Next, use the formula for power: \[ P = F \cdot v \] where \( P \) is the power (in watts), \( F \) is the force (in newtons), and \( v \) is the velocity (in m/s). Rearranging the formula gives us: \[ F = \frac{P}{v} \] Substituting in the values: \[ F = \frac{22380 \, \text{W}}{22.0 \, \text{m/s}} \approx 1017.27 \, \text{N} \] Rounding it, the closest answer is: \( 3) \, 1020 \, \text{N}. \)