Jones is in a real fix again. He is just about to find an incredible treasure, b

Question

Jones is in a real fix again. He is just about to find an incredible treasure, but he
needs your help in order to succeed. He is at the top of a cliff while the treasure is in
a cavern beneath a trap door that is 30 ft below him. The only way Indy can descend
safely is to hold onto a rope wrapped around a large fixed pulley. The other end of
the rope is attached to a bucket with masses in it that serves as a counter balance to
Indy’s 180 pounds, so he can descend without killing himself. When the pulley
begins to turn it triggers a trap door to open 4.00 seconds later for just a short time.
The trap door is covered with sticky glue. If Indy descends too fast or too slow, then
he will stick to the top of the closed trap door where a slobbery dog will lick him continuously with no rescue in sight. In order to control his descent, Indy asks you,
as his trustworthy troll, to calculate the total mass that the bucket and added mass
must be to enable him to achieve a four second descent.

Explanation / Answer

the mass of the bucket should be equal to that of Indy's so that it just balances his weight.

mass of bucket = mass of indy = 180 pounds = m1 (1)

Now, let the added mass (actually mass should be taken out so that the bucket goes up and Indy descents) be m22

so, gravitational force = m1g - m2g = m1a

a = acceleration with which indy descents

=> a = (180 - m2)g/180 (2)

now we have , s = 1/2at2 (equation of motion)

=> 30 = 0.5*{(180 - m2)g/180}*42

=>68.88 = 180 - m2

=> m2 = 111.12 pounds

and Jones gets the treasure ...

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