Question

The velocity v, in meters per second, of a certain type of

wave is given by v(h) = 7h, where h is the depth, in
meters, of the water through which the wave moves.
What is the rate of change of the velocity of the wave with
respect to the depth of the water, when the depth is 5
meters?

Answer 1

The rate of change of the velocity of the wave with respect to the depth is constant at 7 meters per second.

Step-by-step explanation:

The velocity of the wave is given by the equation v(h) = 7h, where h represents the depth of the water. To find the rate of change of velocity with respect to the depth, we can find the derivative of the velocity function with respect to h. Taking the derivative of 7h gives us the rate of change as 7.

Therefore, the rate of change of the velocity of the wave with respect to the depth of the water is constant and equal to 7 meters per second. This means that for every additional meter of depth, the velocity of the wave increases by 7 meters per second.

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