Question

An underwater earthquake produces a tsunami 1,500 km away from Hawaii. If the tsunami travels at \(600 \mathrm{~km} / \mathrm{h}\), how long will it take to reach Hawaii?

Short answer

The tsunami will take 2.5 hours to reach Hawaii.

Step-by-step solution

Understand the Problem

We need to calculate the time it will take for a tsunami to travel a certain distance to Hawaii at a given speed. The tsunami is 1,500 km away and travels at a speed of 600 km/h.

Use the Time Formula

The formula to calculate time when distance and speed are known is \( t = \frac{d}{s} \), where \( t \) is the time, \( d \) is the distance, and \( s \) is the speed.

Substitute Values into the Formula

Substitute the given values into the formula: \( d = 1500 \text{ km} \) and \( s = 600 \text{ km/h} \). So, \( t = \frac{1500}{600} \).

Perform the Calculation

Calculate \( t = \frac{1500}{600} = 2.5 \).

Interpret the Result

The time, \( t \), is equal to 2.5 hours. This means it will take the tsunami 2.5 hours to reach Hawaii.

Key concepts

Distance and Speed Formula

Understanding how to calculate the time it takes for a tsunami to travel a certain distance begins with knowing the distance and speed formula. This basic yet essential formula in physics is expressed as \[ t = \frac{d}{s} \]Here:

• \(t\) represents time,
• \(d\) stands for distance,
• and \(s\) denotes speed.

This equation allows us to find out how long it takes for something to travel from one point to another, given a constant speed. All you need is the total distance and the average speed of the moving object.
For this tsunami example, we use the formula to determine how long the wave takes to cover 1,500 km, maintaining a steady speed of 600 km/h.

Time Calculation

The calculation of time is straightforward if you have the distance and speed of an object. By substituting these known values into the distance and speed formula, you can quickly find the travel time. In our exercise, we substitute

• \(d = 1500\) km,
• and \(s = 600\) km/h,

into the formula, which gives us:\[ t = \frac{1500}{600} \]Performing the division results in \(t = 2.5\), meaning it takes 2.5 hours for the tsunami to reach Hawaii. Calculating time using this method allows you to understand how changes in speed or distance can affect travel time, an invaluable skill in physics and real-world scenarios.

Underwater Earthquake

Underwater earthquakes are powerful natural events that occur when tectonic plates shift beneath the ocean floor. These movements can create a sudden displacement of water, leading to a tsunami. Tsunamis can travel across ocean basins at astonishing speeds, reaching distant coastlines hours after the initial event.
While they're terrifying in potential destructiveness, understanding the dynamics of underwater earthquakes is important for preparedness. Scientists track these activities using various technologies to predict possible tsunami occurrences. This understanding helps in issuing timely warnings, potentially saving lives and reducing panic in affected regions.

Travel Time

The concept of travel time is crucial when dealing with events like a tsunami. Travel time is the duration an object takes to journey from one point to another. In this problem, recognizing the tsunami's travel time allows for effective planning and response.
Using the distance and speed formula, this specific instance computes the time it takes for a tsunami wave to reach Hawaii after an earthquake event. It's instrumental in showing how quick response efforts must be. Knowledge of travel time is also applicable in other fields, such as aviation and logistics, where timely arrivals are key.