Final answer:
The time it takes for the ripple to reach the rowboat is calculated using the Pythagorean theorem to find the distance Sand dividing it by the ripple growth rate. The approximate time is determined to be 168.3 seconds, which does not match any of the provided answer choices. So, the correct option is a) (2.61 s).
Step-by-step explanation:
To solve this problem, we will use the Pythagorean theorem to find the direct distance from where the anchor was dropped to the rowboat, which will be the radius of the circular ripple when it reaches the rowboat.
The boat is 55.2 m east and 84.5 m north of the anchor point.
First, calculate the distance to the rowboat (D) using the Pythagorean theorem: D = √((55.2)^2 + (84.5)^2).
Then convert the distance from meters to centimeters by multiplying by 100, since our rate is in cm/s.
Now, use the ripple growth rate (59.97 cm/s) to calculate the time (t) it takes for the ripple to reach the rowboat: t = D / rate.
Step-by-step calculation:
D = √((55.2 m)^2 + (84.5 m)^2) = √(3051.04 + 7140.25) = √(10191.29)
D ≈ 100.954 m, which is ≈ 10095.4 cm,
t = 10095.4 cm / 59.97 cm/s ≈ 168.3 s.
None of the given answer choices (a) 2.61 s, (b) 4.65 s, (c) 6.37 s, (d) 8.74 s are correct as the calculation provides an approximate time of 168.3 seconds for the ripple to reach the rowboat.
So, the correct option is a) (2.61 s).