Chapter 5.2, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

Bores Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge of water much like what would be expected if a dam failed suddenly and emptied a reservoir in to a river bed. In the case of a bore travelling from the ocean into a dry river bed, one study shows that the velocity $V$ of the tip of the bore is proportional to the square root of its height $h$. Expressed in a formula, this is

$V=k{h}^{0.5}$,

where $k$ is a constant.

a. A bore travels up a dry river bed. How does the velocity of the tip compare with its initial velocity when its height is reduced to half of its initial height?

b. How does the height of the bore compare with its initial height when the velocity of the tip is reduced to half of its initial velocity?

c. If the tip of one bore surging up a dry river bed is three times the height of another, how do their velocities compare?