The time it takes for a tsunami with a wavelength of 6.50 × 10⁴ m and a period of 12.0 minutes to travel from Japan to California across the Pacific Ocean is approximately 24.62 hours.
To calculate the time it takes for a tsunami to travel from Japan to California, we first need to determine the speed of the tsunami. Given a wavelength (λ) of 6.50 × 10⁴ m and a period (T) of 12.0 minutes, we can use the formula for wave speed, v = λ / T, where λ is the wavelength and T is the period. However, the period must be in seconds, so we convert 12.0 minutes to 720 seconds (12 × 60).
The speed of the tsunami is then calculated as follows: v = (6.50 × 10⁴ m) / (720 s) = 90.28 m/s. We now have the speed of the tsunami in meters per second, which we can use to calculate the travel time across the Pacific Ocean. To do this, we convert the distance from Japan to California from kilometers to meters: 8.00 × 10³ km = 8.00 × 10⁶ m.
The time taken (t) to travel 8.00 × 10⁶ m at a speed of 90.28 m/s can be found using the formula t = distance / speed, which is t = (8.00 × 10⁶ m) / (90.28 m/s). Calculating this provides us with a travel time of approximately 88633.57 seconds, or roughly 24.62 hours when converted back to hours (since 1 hour = 3600 seconds).
Therefore, it takes approximately 24.62 hours for the tsunami to travel from Japan to California across the Pacific Ocean.