Tsunami Speed Calculation

The speed of a tsunami wave depends primarily on the ocean depth. The formula for shallow water wave speed is:

$ v = \sqrt{g \times h} $

Where:

• v is the wave speed
• g is the acceleration due to gravity (approximately $9.8 \text{ m/s}^2$)
• h is the water depth

Calculating Wave Speed

Given:

• Distance ($d$) = 1000 km
• Water depth ($h$) = 6.25 km

First, convert the water depth to meters:

$ h = 6.25 \text{ km} = 6.25 \times 1000 \text{ m} = 6250 \text{ m} $

Now, calculate the wave speed using $g \approx 9.8 \text{ m/s}^2$:

$ v = \sqrt{9.8 \text{ m/s}^2 \times 6250 \text{ m}} = \sqrt{61250 \text{ m}^2/\text{s}^2} \approx 247.5 \text{ m/s} $

Determining Arrival Time

Convert the speed from m/s to km/hr for easier time calculation:

$ v \approx 247.5 \text{ m/s} \times \frac{3600 \text{ s}}{1 \text{ hr}} \times \frac{1 \text{ km}}{1000 \text{ m}} \approx 891 \text{ km/hr} $

Calculate the time taken to reach the shore using the formula Time = Distance / Speed:

$ t = \frac{d}{v} = \frac{1000 \text{ km}}{891 \text{ km/hr}} \approx 1.12 \text{ hours} $

This calculated time is approximately 1.12 hours. Among the given options, 1 hour is the closest value.