Final answer:
The work performed by the winch to pull the 3500-lb vehicle 30 feet is 105795 ft-lbs.
Step-by-step explanation:
The work done by the winch can be calculated using the formula:
Work = Force x Distance
In this case, the force exerted by the winch is equal to the weight of the vehicle, which is 3500 lbs (converted to mass by dividing by the acceleration due to gravity, approximately 32.2 ft/s^2). The distance is given as 30 feet. So, the work done is:
Work = 3500 lbs / 32.2 ft/s^2 x 30 feet
Converting the units to pounds-force and feet:
Work = (3500 lbs / 32.2) x (30 x 32.2) ft-lbs
Work = 105795 ft-lbs
Therefore, the work performed by the winch to pull the 3500-lb vehicle 30 feet is 105795 ft-lbs.