Substitute 500 for the water depth d in the given formula. Then, find the square root of the simplified expression.
B
Substitute different values for the water depth in the given formula. Is there a relationship between water depth and the speed of the tsunami?
A
70 meters per second
B
The speed of the tsunami decreases as the water depth decreases, see solution.
Practice makes perfect
We want to find the speed of a tsunami when the water depth is 500 meters using the given equation.
s=sqrt(9.8d)
In this formula, s is the speed of the tsunami in meters per second and d is the water depth in meters. From the exercise, we know that the water depth is 500 meters. To find the speed of the tsunami, we will substitute 500 for d in the given formula and solve for s. Let's do it!
We found that the speed of the tsunami is 70 meters per second. Notice that we do not have to consider the negative root because speed cannot be negative.
We want to know what happens to the speed of the tsunami as the water depth decreases. Let's make a table of values to find the speed s of the tsunami at various depths d. Then, we will look for a relationship between the speed of the tsunami and the water depth. Let's do it!
Water Depth, d
Substitution Into Formula
Speed of the Tsunami, s
500
s=sqrt(9.8( 500))
70
400
s=sqrt(9.8( 400))
≈ 63
300
s=sqrt(9.8( 300))
≈ 54
200
s=sqrt(9.8( 200))
≈ 44
100
s=sqrt(9.8( 100))
≈ 31
Looking at the table, we can see that as the water depth decreases, the speed of the tsunami also decreases.
