A rocket is propelled by a force of 106 N and has a speed of 3000 m/s. What is the power expended?

Question

ScanSolve AI Tutor · Accepted Answer

To determine the power expended, we use the formula that relates power, force, and velocity.

Identify the given values.
The force propelling the rocket is $F = 10^6 \, \text{N}$ .
The speed acquired by the rocket is $v = 3000 \, \text{m/s}$ .
The mass of the rocket is $m = 40,000 \, \text{kg}$ (this information is not needed for calculating power directly from force and velocity).
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:
$P = F \cdot v$
Substitute the given values into the formula and calculate the power.
$P = (10^6 \, \text{N}) \times (3000 \, \text{m/s})$ $P = 3000 \times 10^6 \, \text{W}$
To express this in scientific notation:
$P = 3 \times 10^3 \times 10^6 \, \text{W}$ $P = 3 \times 10^{(3+6)} \, \text{W}$ $P = 3 \times 10^9 \, \text{W}$
Compare the result with the given options.
The calculated power is $3 \times 10^9 \, \text{watts}$ . This matches option D.

The final answer is $\text{D. } 3 \times 10^9 \text{ watts}$ .

Answer