Question

The speed that a tsunami (tidal wave) can travel is modeled by the equationmc001-1.jpgwhere S is the speed in kilometers per hour, and d is the average depth of the water in kilometers.
A tsunami is traveling at 140 km/hr. What is the approximate average depth of the water?

0.133 km

0.145 km

0.155 km

Answer 1

Tsunami speed in deep water: c = sqrt(g d). With g = 9.8 m/s^2, convert units to get S (km/hr):

S = 3600·sqrt(0.0098·d) ≈ 356.4·sqrt(d).

So sqrt(d) = 140/356.4 ≈ 0.3928, hence d ≈ 0.3928^2 ≈ 0.1543 km ≈ 0.155 km.

Answer: 0.155 km.