Answer :
Final answer:
The shortest time in which the crane can lift the load over a distance of 79.0 m is approximately 54.4 seconds.
Explanation:
To find the shortest time in which the crane can lift the load, we need to calculate the power required and then use it to calculate the time. The power required can be calculated by multiplying the weight of the load by the distance it needs to be lifted divided by the time. In this case, the power required is 67% of the maximum hoisting power of the crane's motor, which is 163 hp. So, the power required is 0.67 * 163 = 109.21 hp. To find the time, we divide the work done (power required multiplied by time) by the power required. The work done is given by the formula work = force * distance. In this case, the force is the weight of the load (5750 kg * 9.8 m/s^2) and the distance is 79.0 m. So, the work done is (5750 kg * 9.8 m/s^2) * 79.0 m = 4,437,725 J. Dividing the work done by the power required, we get the time in seconds: 4,437,725 J / (109.21 hp * 746 W/hp) = 54.4 seconds. Therefore, the shortest time in which the crane can lift the load over a distance of 79.0 m is approximately 54.4 seconds.
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