Final answer:
The speed of the rocket is found by comparing the times and distances at which cannons a and b shoot and the fact that the shots are detected simultaneously. Using the distance from cannon b to the rocket and the known time delay, we calculate the rocket's speed to be 1.5 km/s.
Step-by-step explanation:
To determine the speed of the rocket, we need to consider the difference in both time and distance for the shots fired from cannons a and b. Cannon fires at t=0 and is positioned at Xa=0 km, while cannon b fires at t=1 μs (1×10-6 seconds) and is positioned at Xb=1.5 km. The fact that the rocket detects both shots at the same time indicates that the rocket is moving toward the cannons at a certain speed.
Let's denote the speed of the rocket as Vr. Since the rocket detects both shots at the same time, the time taken by the shot from cannon a to reach the rocket should equal the time taken by the shot from cannon b plus the time delay in b's shot (1×10⁻⁶ seconds). We can express this as:
Distance / Speed = Time
1.5 km / Vr = (0 km / Vr) + 1×10⁻⁶ s
To solve for the rocket's speed, we rearrange the equation:
1.5 km = Vr × 1×10⁻⁶ s
Therefore, the rocket's speed, Vr, can be calculated as:
Vr = 1.5 km / 1×10⁻⁶ s = 1.5×10⁶ km/s = 1.5 km/μs
The correct answer is A) 1.5 km/s.