We have an ultrasonic speed measurement setup. A detector sends ultrasonic pulses to a moving car every second. The first pulse is sent at t equals zero, its echo is received at t equals one second when the second pulse is sent, and the second echo is received at t equals one point nine seconds. We need to determine if the car is approaching or moving away from the detector.
Let's analyze the echo times. The first pulse travels to the car and back in one second, while the second pulse takes one point nine seconds for the round trip. Since the second echo takes longer, the distance to the car has increased. This means the car is moving away from the detector. We can express this mathematically: the round trip time equals two times the distance divided by the sound speed.
Now let's calculate the actual distances. Using the sound speed of three hundred forty meters per second, we can find the car's position at each time. For the first measurement, distance equals one second times three hundred forty meters per second divided by two, which gives us one hundred seventy meters. For the second measurement, distance equals one point nine seconds times three hundred forty divided by two, giving us three hundred twenty-three meters.
Now we can calculate the car's speed. The car moved from one hundred seventy meters to three hundred twenty-three meters in one second. The distance traveled is three hundred twenty-three minus one hundred seventy, which equals one hundred fifty-three meters. Since this happened in exactly one second, the car's speed is one hundred fifty-three meters per second.