# A woman carries a bucket to the top of a 40 m tower...

by iamkristing
Tags: bucket, carries, solved, tower, woman
 P: 280 For the first part, you know that the vertical speed is constant, and the leakage is constant. Also you were given start and end values for the mass of the water so you can calculate how much water was lost in total. Therefore you can deduce that when half of the total lost water was lost, she was half way up, and when 3/4 of the total lost water was lost she was 3/4 up etc. So you can consider height and mass of water loss as directly proportional to one another: $$h \propto m$$ Therefore: $$h = km$$ Where k is some constant you can calculate from known values of height and water loss. That will get you pretty close to your answer, but what you need to find is an equation for the mass of the water left plus the mass of the bucket, I'll let you see if you can take it from here though. For the second part, you could just say that since the water loss is constant, you can use the average mass of the water in the bucket plus the mass of the bucket and plug it into the formula: $$GPE = mgh$$