Suppose that a wave forms in shallow water. Then the depth d of the water (in meters) and the velocity of the wave (in meters per second) are related by the equation√98d. If a wave formed in shallow water has a velocity of 5.1 meters per second, what is the water's depth?
The equation that relates the depth d of the water and the velocity of the wave is given as √98d = v, where v is the velocity of the wave.
To find the water's depth, we need to solve the equation for d.
√98d = v
Squaring both sides to eliminate the square root:
98d = v^2
Dividing both sides by 98:
d = v^2/98
Substituting the given velocity, v = 5.1 meters per second, into the equation:
d = (5.1^2) / 98
d = 26.01 / 98
d ≈ 0.2652 meters
Therefore, the water's depth is approximately 0.2652 meters.