Question

A radar is being calibrated and is tracking an aircraft approaching head-on. the radar's first pulse transmitted at t = 0 returns 21.54μs after it is transmitted and the second pulse transmitted at t = 1s returns 21.18μs after it is transmitted. knowing that the pulses were 1 second apart, what is the computed speed of the aircraft

Answer 1

The computed speed of the aircraft is 54 m/s.

Step-by-step explanation:

To calculate the speed of the aircraft, we can use the formula:

Speed = Distance / Time

Since the radar measures the round-trip time for the pulse, we need to divide the time by 2 to get the one-way time. In this case, the first pulse returned after 21.54 μs, which means the one-way time is 10.77 μs. The second pulse returned after 21.18 μs, which means the one-way time is 10.59 μs.

Using the fact that the pulses were transmitted 1 second apart, we can subtract the two one-way times to find the time it takes for the aircraft to travel the distance between the two pulses.

Time = 10.77 μs - 10.59 μs = 0.18 μs

Next, we can use the formula for speed to find the distance traveled:

Speed = Distance / Time

1 second = 0.18 μs + Distance / Speed

Distance = (Speed)(Time)

Distance = (3.00 × 10^8 m/s)(0.18 × 10^-6 s) = 54 m

Therefore, the computed speed of the aircraft is 54 m/s.