A group of swimmers is resting in the sun on
an off-shore raft. They estimate that 2.85 m
separate a trough and an adjacent crest of
surface waves on the lake. They count 13
crests that pass by the raft in 20 s.
How fast are the waves moving?
Well, I must say, those waves are really making a splash! To calculate the speed of the waves, we need to divide the distance between the trough and a crest by the time it takes for one wave to pass by. So, by dividing 2.85 m by 13 crests, we get the distance between each wave. That would be approximately 0.219 m. Now, since 20 seconds passed for 13 waves to pass by, we can divide 0.219 m by 20 s to get the speed of the waves. And voila! The speed of the waves is about 0.011 m/s. Those waves might not be breaking any records, but they sure know how to keep things wavy!
To find the speed of the waves, we can use the formula:
Speed = Distance / Time
In this case, the distance between the trough and the adjacent crest is given as 2.85 m. The time is given as 20 seconds. However, we need to determine the distance covered by one wave crest in 20 seconds.
To find the distance covered by one wave crest, we can divide the total distance (2.85 m) by the number of crests that pass by the raft in 20 seconds (13 crests).
Distance covered by one wave crest = 2.85 m / 13 crests
Now, we can calculate the speed of the waves using the formula mentioned above:
Speed = (2.85 m / 13 crests) / 20 s
Simplifying the equation:
Speed = 2.85 m / (13 crests * 20 s)
Speed = 2.85 m / (260 crests * s)
Speed ≈ 0.011 m/s
Therefore, the waves are moving at a speed of about 0.011 m/s.
To find the speed of the waves, we can use the formula:
Speed = Distance/Time
First, let's find the distance between two adjacent crests. We are given that 2.85 m separates a trough and an adjacent crest. Since a wave consists of a crest and a trough, the distance between two adjacent crests would be twice the given distance, which is 2 * 2.85 m = 5.7 m.
Now, we know that 13 crests pass by the raft in 20 seconds. This means that 13 crests travel a distance of 5.7 m in 20 seconds.
Speed = Distance/Time
Speed = (13 crests * 5.7 m)/20 s
To calculate the speed, we multiply the number of crests by the distance between them and then divide by the time taken.
Speed = (13 * 5.7)/20
Speed = 74.55/20
Speed ≈ 3.728 m/s
Therefore, the waves are estimated to be moving at approximately 3.728 m/s.