A speed boat requires 80 kW to move at a constant speed of \( 15 \mathrm{~m} / \mathrm{s} \). What is the resistive force of the water at this speed? 1) 2700 N 2) 5300 N 3) 6500 N 4) 7700 N 5) 8400 N

To find the resistive force of the water, we can use the formula for power, which is given by: \[ P = F \cdot v \] Where \( P \) is the power (in watts), \( F \) is the force (in newtons), and \( v \) is the speed (in meters per second). Rearranging the formula to solve for force \( F \): \[ F = \frac{P}{v} \] Substituting the values: \[ F = \frac{80,000 \, \text{W}}{15 \, \text{m/s}} = \frac{80,000}{15} \approx 5333.33 \, \text{N} \] So, the resistive force is approximately 5300 N. The answer is 2) 5300 N. For some real-world spark: Boats have had a rough ride since ancient times faced with wind and water resistance. Sailors initially relied on nature's elements. Fast forward to now, and we have powerful engines and hydrodynamic designs to cut through water, proving that innovation fuels our need for speed! And don’t forget! Always check units when dealing with physical equations. A common mistake is to mix watts (W) with kilowatts (kW) or to overlook the speed conversion. Always keep your units aligned for smooth sailing through physics problems!