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Given: Power at 285 m (P1) = 45 W Distance from the Base Station (d1) = 285 m Distance from the Base Station (d2)
Given: Power at 285 m (P1) = 45 W Distance from the Base Station (d1) = 285 m Distance from the Base Station (d2) = 1.14 km = 1140 m Using the inverse 4th power law, the relationship between power (P) and distance (d) is given by: P1/P2 (d2/d1)4 Substituting the given values, we have: 45 W/P2 (1140 m / 285 m) P2 = 45 W/ (1140 m / 285 m)4 Calculating the value of P2: P2 = 45 W / (1140 m / 285 m) P2 = 45 W / (4) P2 = 45 W / 256 P2 = 0.1758 W Given: Power at 1.14 km (P2) = 0.1758 W To convert the power from W to scientific notation, we use the following steps: 1. Move the decimal point to the left until there is only one digit to the left of the decimal point. This represents the coefficient. 2. Count the number of places you moved the decimal point. This will be the exponent of 10. In this case, we move the decimal point two places to the left to get 1.758 W. The exponent of 10 is 2. So, the power at 1.14 km is 1.758 x 10^(-2) W. formula, we have: d2 d1 * (P1 P2)^(1/4) Substituting the given values, we have: d2 = 285 m * (45 W/ 1.758 x 10^(-2) W)^(1/4) Calculating the distance d2: d2 = 285 m (45 W/1.758 x 10^(-2) W)^(1/4) d2 = 285 m (45/1.758)^(1/4) d2 = 285 m (25.6)^(1/4) d2 = 285 m 2.13 d2 = 606.45 m Converting the distance from meters to kilometers: d2 = 606.45 m / 1000 m/km d2 = 0.60645 km i. The reasonable power value at 1.14 km from the Base Station is approximately 1.758 x 10^(-2) W. ii. The distance from the Base Station, given the received signal strength of 72 nW, is approximately 0.61 km.
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