This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To determine the power expended, we use the formula that relates power, force, and velocity. Step 1: Identify the given values. The force propelling the rocket is F = 10^6 \, N. The speed acquired by the rocket is v = 3000 \, m/s. The mass of the rocket is m = 40,000 \, kg (this information is not needed for calculating power directly from force and velocity). Step 2: Recall the formula for power. Power (P) is defined as the rate at which work is done, or the product of force and velocity when the force is applied in the direction of motion: P = F · v Step 3: Substitute the given values into the formula and calculate the power. P = (10^6 \, N) × (3000 \, m/s) P = 3000 × 10^6 \, W To express this in scientific notation: P = 3 × 10^3 × 10^6 \, W P = 3 × 10^(3+6) \, W P = 3 × 10^9 \, W Step 4: Compare the result with the given options. The calculated power is 3 × 10^9 \, watts. This matches option D. The final answer is D. 3 × 10^9 watts.