1. Water drops are being dropped into a body of water at a rate of 43 drops every 60 s. The distance between a crest and the seventh crest ahead of it is 2.40 m. Find the speed at which the waves are travelling.
To find the speed at which the waves are traveling, we can use the formula:
Speed = Distance / Time
In this case, the distance between the crests is given as 2.40 meters. Now, let's find the time it takes to complete 7 crests.
Given that 43 drops are being dropped every 60 seconds, we can calculate the time it takes for 7 crests using the drop rate. Since every drop creates a crest, we can assume that the drop rate is the same as the crest rate.
The number of crest drops in 60 seconds is given by:
43 drops / 60 s = x drops / 7 s
To find 'x' (drops in 7 seconds), we can rearrange the equation:
x = (43 drops / 60 s) * 7 s
x = 43 * 7 / 60
x = 5.03 drops
So, it takes 5.03 drops to complete 7 crests.
Now, let's calculate the time it takes for 7 crests:
Time = number of crests / drop rate
Time = 7 crests / 5.03 drops
Simplifying this, we get:
Time = 1.39 seconds
Finally, we can calculate the speed of the waves:
Speed = Distance / Time
Speed = 2.40 m / 1.39 s
Speed ≈ 1.727 m/s
Therefore, the speed at which the waves are traveling is approximately 1.727 m/s.