A radar is able to detect the reflected waves from an enemy aeroplane after a time interval of 0.02 millisecond. If the velocity of the waves is 3 × 108ms−1 , calculate the distance of aeroplane from the radar (in km ).
Question
A radar is able to detect the reflected waves from an enemy aeroplane after a time interval of 0.02 millisecond. If the velocity of the waves is 3 × 108ms−1 , calculate the distance of aeroplane from the radar (in km ).
Solution
Sure, here's how to solve this problem:
Step 1: Convert the time from milliseconds to seconds. 0.02 milliseconds = 0.02 x 10^-3 seconds = 2 x 10^-5 seconds
Step 2: The total distance covered by the radar waves is the product of the speed of light (the speed of the radar waves) and the time it takes for the waves to return to the radar. Distance = Speed x Time Distance = 3 x 10^8 m/s x 2 x 10^-5 s = 6000 meters
Step 3: However, this is the total distance covered by the radar waves, which includes the distance from the radar to the airplane and back. Since we want to find the distance from the radar to the airplane, we need to divide the total distance by 2. Distance to airplane = Total Distance / 2 Distance to airplane = 6000 m / 2 = 3000 meters
Step 4: Convert the distance from meters to kilometers. 3000 meters = 3 kilometers
So, the airplane is 3 kilometers away from the radar.
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