Question

A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. The Pacific Tsunami Warning Center is responsible for monitoring earthquakes that could potentially cause tsunamis in the Pacific Ocean. Through measuring the water level and calculating the speed of a tsunami, scientists can predict arrival times of tsunamis. The speed \(s\) (in meters per second) at which a tsunami moves is determined by the depth \(d\) (in meters) of the ocean. \(s=\sqrt{g d},\) where \(g\) is 9.8 meters per second per second. Find the speed of a tsunami in a region of the ocean that is 1000 meters deep. Write the result in simplified form.

Short answer

The speed of the tsunami in a region of the ocean 1000 meters deep is 99.0 meters per second.

Step-by-step solution

Understand the Given Variables

The depth of the ocean \(d\) is given as 1000 meters. The gravitational constant \(g\) is known to be 9.8 meters per second per second.

Substitute the Values into the Formula

The formula for the speed of a tsunami is \(s=\sqrt{g d}\). So plug in the values to get: \(s=\sqrt{9.8 \times 1000}\).

Solve the Equation

Solving the equation \(s=\sqrt{9.8 \times 1000}\) will give the speed of the tsunami. Square roots are typically used for this type of calculation. So, doing the calculations we get \(s = 99.0\) meters per second.