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Question
A RADAR sends a signal with a speed of 3 x 108 m s-1 to an aeroplane at a distance of 300 km from it. After how much time is the signal received back after reflection from the aeroplane?
Solution
Given, d = 300 km
Converting km to m, we get,
1 km = 1000 m
Therefore, 300 km = 3,00,000 m
Hence, d = 3 × 105 m
Speed of sound transmitted from RADAR (V) = 3 × 108 m/s
Since the signal travels twice, that is, when transmitted and when it is being received by the RADAR, the distance is calculated twice i.e. 2d
As we know,
Speed of Sound (V) = `"Total distance travelled (2d)"/("Time interval " ("t")`
∴ `3 xx 10^8 = (2 xx (3 xx 10^5))/("t")`
∴ t = `(2 xx (3 xx 10^5))/(3 xx 10^8)`
∴ t = `2/10^3`
∴ t = 2 × 10-3 s
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