Question 1082940: A man lifts a bag of sand to a scaffold 30 above his head by means of a rope which passes over a pulley on the scaffold. The rope is 60 m long. If he keeps his end of the rope horizontal and walks away from beneath the pulley at 4 meters per second, how fast is the bag rising when he is 22.5 meters away?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! the vertical speed of the bucket is the same as the speed at which the amount of rope (call it z) between the pulley and his end of the rope increases. In other words, the rope is not elastic.
Make a drawing and you'll get a triangle where z is the hypotenuse. Let x be the horizontal position, and you have that:
z=(√102+x2)
Take the derivative of z with respect to time and you get the speed vz, which is the answer you are looking for, the rate at which the bag is rising.
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