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 into a river bed. In the case of a bore traveling from the ocean into a dry river bed, one research study shows that the velocity V of the tip of the bore is proportional to the square root of its height H. The power function formula is given below, where k is a constant. V = k* H 0.5 (a) A bore travels up a dry river bed. By how much does the wave velocity change when its height is reduced to a half of its initial height? The velocity changes by a factor of (b) By how much does the bore height change when the velocity of the tip is reduced to a quarter of its initial velocity? The height is reduced to of the initial height. (c) If the tip of one bore surging up a dry river bed is two times the height of another, how do their velocities compare? The velocity of the first is times that of the other.