Question

in august of 1883, a volcano erupted on the island of krakatau, indonesia, causing a tsunami that traveled into the indian ocean. the speed s (in kilometers per hour) that a tsunami travels can be modeled by the formula: s = 356√d where d is the depth (in kilometers) of the water. if a tsunami from krakatau hit jakarta traveling at about 60 kilometers per hour, what is the average depth of the water between krakatau and jakarta? 0.025 kilometers 0.028 kilometers 0.030 kilometers 0.035 kilometers

Explanation:

Step1: Substitute speed value

Given $s = 356\sqrt{d}$ and $s = 60$. Substitute $s$ into the formula: $60=356\sqrt{d}$.

Step2: Solve for $\sqrt{d}$

Divide both sides by 356: $\sqrt{d}=\frac{60}{356}=\frac{15}{89}$.

Step3: Solve for $d$

Square both sides: $d = (\frac{15}{89})^2=\frac{225}{7921}\approx0.028$.

Answer:

0.028 kilometers