Power P = 1/f (in metre). f = 1/P = 1/2 = 0.5 m = 50 cm. Positive power indicates convex lens. For concave lens, power negative. Dioptre (D) is SI unit of power. Remember f in metres.
Explanation:
The maximum height H = (u^2 * sin^2(theta)) / 2g. The horizontal range R = (u^2 * sin(2theta)) / g. For an angle of 45 degrees, sin(45) = 1/sqrt(2) and sin(90) = 1. H = (u^2 * 0.5) / 2g = u^2 / 4g. R = u^2 / g. Therefore, H/R = (u^2/4g) / (u^2/g) = 1/4. The ratio is 1:4.
Explanation:
Speed = distance/time = 100 m / 5 s = 20 m/s. Convert to km/h: multiply by 18/5 => 20 × 18/5 = 72 km/h. Pole is a point, so train's own length is the distance crossed. Speed in km/h = m/s × (18/5). 20 × 18/5 = 72.
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