Question

Suppose that a wave forms in shallow water. The depth of the water d (in feet) and the velocity of the wave v (in feet per second) are related by the equation v = sqrt 32d. If a wave forms in water with a depth of 8.5 feet, what is its velocity?

Answer 1

To find the wave velocity in shallow water with a depth of 8.5 feet, we use the equation v = √(32d) and calculate the square root of 32 × 8.5, yielding the wave's velocity = 16.49 feet per square .

Step-by-step explanation:

To find the velocity of the wave in shallow water, we use the given relationship v = √(32 d), where v is the velocity in feet per second and d is the depth in feet.

For a wave forming in water with a depth of 8.5 feet, we substitute d with 8.5 in the equation:

v = √(32 × 8.5)

We then calculate the square root of the product of 32 and 8.5 to find the wave velocity.

Thus, the velocity of the wave (v) is √(32 × 8.5) feet per second.

v ≈ 16.49 feet per second

Answer 2

Its velocity is 16.5 feet/sec

Step-by-step explanation:

Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation

v = √(32d)

a wave forms in water with a depth of 8.5 feet, therefore d = 8.5 ft

velocity = √(32 x 8.5)

= √272

= 16.49 feet/sec

≈ 16.5 ft/s