Final answer:
The magnitude of the acceleration of the weight swung in a circle on a piece of fishing line is calculated using the centripetal acceleration formula. After performing the calculation, the resulting acceleration is 26.45 m/s², which does not match any of the provided options.
Step-by-step explanation:
The question at hand involves calculating the centripetal acceleration of a weight being swung in a circle at the end of a fishing line. When an object is moving in a circular path, it experiences centripetal acceleration which is directed towards the center of the circle. The formula to calculate the centripetal acceleration (a) is: a = (v^2) / r, where v is the tangential speed of the object and r is the radius of the circle.
To calculate the tangential speed, we can use the formula v = (2πr) / T, where T is the period of one complete rotation. For a fishing sinker weight making a complete circle every 0.90 seconds with a 0.55-meter piece of fishing line, we first find the speed (v) using the given radius (r = 0.55 m) and period (T = 0.90 s).
v = (2π(0.55 m)) / 0.90 s = (3.433 m) / 0.90 s = 3.814 m/s
Now, apply this speed to the formula for centripetal acceleration:
a = (3.814 m/s)^2 / 0.55 m = 14.5465 m^2/s^2 / 0.55 m = 26.45 m/s²
After calculating the result, it appears that there is no matching option in the multiple-choice answers provided by the student. It is essential to double-check the work to ensure accuracy since none of the given options are correct based on the calculation performed.