Final answer:
To find the required sling length for an object to travel at 46 m/s given an angular velocity of 92 rpm, convert the rotational rate to radians per second and use the linear velocity equation. This gives us a sling length of 4.79 meters, which does not match any of the provided multiple choice options.
Step-by-step explanation:
To determine the length of the sling so that the speed of the object at the end will be 46 meters per second, we must first convert the given rotational speed from revolutions per minute (rpm) to radians per second. There are 2π radians in one revolution and 60 seconds in one minute. Hence, the angular velocity (ω) in radians per second is:
ω = 92 rpm × (2π rad/rev) × (1 min/60 s) = 9.6 rad/s
The linear velocity (v) of the object on the sling relates to the angular velocity (ω) and the radius (or length, r) of the sling's rotation by the equation v = rω. To find the length, we rearrange this equation to solve for r:
r = v/ω = 46 m/s / 9.6 rad/s = 4.79 m
Since the possible answers are in whole meters and 4.79 m is not an option, we can conclude that there's probably been a typo or mistake in the provided options, as none of them match the calculated result.