2020 · Q42
When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m?
Elementary MathematicsRatio and Proportion
- A5 seconds
- B5.5 seconds
- C6 seconds
- D6.5 seconds
Explanation
t = k*sqrt(d), so t = 4*sqrt(122.5/78.4) = 4*1.25 = 5 seconds - option (A).In general t2/t1 = sqrt(d2/d1), so t = 4*sqrt(1.5625) = 4*1.25. The ratio of the distances is 122.5/78.4 = 1.5625 = (1.25)^2.