Aleaky 10-kg bucket is lifted from the ground to a height of 16 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 48 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 16-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.)

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The mass comes in three parts:

Both the mass of the rope and the mass of the water in the bucket varies with the height of the bucket. Express the two masses as a function of :

The water in the bucket behaves like yet another rope of density . The mass of the water left in the bucket at height will be

The mass of the bucket is . Combining the three:

Weight of the bucket at height :

The bucket moves upward at a constant speed. As a result,

Express the work required as a definite integral:

Rewrite the definite integral as a Riemann Sum:

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

reserve is the answer