When earthquakes occur under the sea, they can cause large tidal waves called tsunamis - Leaving Cert Mathematics - Question 9 - 2018

The tsunami is 400 km from land. We first convert this distance into metres:

$400 \, \text{km} = 400000 \, \text{m}$

Using the speed $s = 140 \, \text{m/s}$, we calculate the time $t$ it takes to travel this distance using the formula:

$t = \frac{\text{distance}}{\text{speed}} = \frac{400000}{140}$

Calculating the time:

$t = 2857.14 \, \text{s}$

To convert seconds into minutes:

$\text{minutes} = \frac{2857.14}{60} \approx 47.62 \, \text{minutes}$

Rounding to the nearest minute gives approximately:

$48 \, \text{minutes}$

Starting from the original formula:

$s = \sqrt{g \times d}$

We square both sides:

$s^2 = g \times d$

Next, we rearrange for $d$:

$d = \frac{s^2}{g}$

Using the rearranged formula:

$d = \frac{s^2}{g}$

Substituting $s = 55 \, \text{m/s}$ and $g = 9.8 \, \text{m/s}^2$:

$d = \frac{55^2}{9.8}$

Calculating this gives:

$d = \frac{3025}{9.8} \approx 308.16 \, \text{m}$

Rounding to the nearest metre gives:

$d = 308 \, ext{m}$