Final answer:
To pull in 1 meter of rope with a 9-inch diameter winch, the winch must be turned approximately 501 degrees. This calculation is based on the circumference of the winch and the length of rope collected per rotation.
Step-by-step explanation:
Calculating the Rotation needed for a Winch to Pull in 1 Meter of Rope
To determine how much a 9-inch diameter winch should be turned to pull in 1 meter of rope, we need to calculate the circumference of the winch and then use that to establish how much rotation is necessary. The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle. Converting the diameter to meters, we have 9 inches which is approximately 0.2286 meters. The circumference C is then π * 0.2286 m = 0.7184 meters.
To pull in 1 meter of rope, we need to consider the length of the rope that is wound per each complete rotation of the winch. As each rotation pulls in 0.7184 meters of rope, we can find the number of degrees for 1 meter by dividing 1 meter by the circumference and then multiplying by 360 degrees, which is a full rotation. Therefore, the winch should be turned by (1/0.7184) * 360 degrees, which equates to approximately 501 degrees. However, the information given in the reference solution seems to be irrelevant or incorrect, as it does not match the pattern of solving the question about the winch and the rope.