A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter tall building. You have a rope that has a mass of 0.1 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 8 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building.

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A: Solution :-

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A: Let's understand what's going on:

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Q: Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 40 cm to a…

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Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

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A:

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A: Topic = Volume

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A:

Q: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

A: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

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A:

Q: A ladder 15 feet long leans against a vertical wall. If the bottom of the ladder is pulled away from…

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A: Solution of the problem as follows

Q: A 10 ft long ladder rests against a vertical wall. If the top of the ladder slides down from the…

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Q: A ladder of length 5 m rests against a vertical wall. If the base of the ladder is pulled away from…

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Q: A ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

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A:

Q: A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.