Question

in 2004, a massive earthquake off the coast of sumatra, indonesia, triggered a tsunami that affected many countries around the indian ocean. the speed s (in kilometers per hour) of the tsunami can be modeled by the formula: $s = 356sqrt{d}$ where d is the depth (in kilometers) of the ocean. if a tsunami from the earthquake reached the coast of thailand traveling at approximately 80 kilometers per hour, what is the average depth of the water in that area? 0.045 kilometers 0.040 kilometers 0.050 kilometers 0.055 kilometers

Explanation:

Step1: Substitute speed value

Given $s = 356\sqrt{d}$ and $s = 80$. So, $80=356\sqrt{d}$.

Step2: Isolate square - root term

Divide both sides by 356: $\sqrt{d}=\frac{80}{356}=\frac{20}{89}$.

Step3: Solve for d

Square both sides: $d = (\frac{20}{89})^2=\frac{400}{7921}\approx0.050$.

Answer:

0.050 kilometers