Final answer:
The speed of the weight at the end of the rope is calculated using the formula v = √(ac × r), where ac is the centripetal acceleration and r is the radius. The correct calculation results in a speed of 4.53 m/s, which corresponds to option (a).
Step-by-step explanation:
The student's question asks for the speed of a weight spinning in a circle at the end of a rope, based on given values for rope length and centripetal acceleration. This problem is closely related to the concept of centripetal force in physics, which is the force that acts on an object moving in a circular path and is directed towards the center around which the object is moving. The formula to calculate the speed (v) of the object is v = √(ac × r), where ac is the centripetal acceleration and r is the radius of the circle.
Given: ac = 16.4 m/s² and r = 1.25 m.
Plugging these values into the formula gives v = √(16.4 m/s² × 1.25 m), which calculates to v = √20.5 and approximates to v = 4.53 m/s. Thus, the speed of the weight at the end of Haley's rope is approximately 4.53 m/s, which corresponds to option (a) from the given choices.