A painter is standing on scaffolding that is raised at constant speed. As he tra

Question

A painter is standing on scaffolding that is raised at constant speed. As he travels upward, he accidentally nudges a paint can off the scaffolding and it falls a distance 15.9 m to the ground. You are watching, and measure with your stopwatch that it takes a time of 3.26 s for the can to reach the ground. Ignore air resistance.

What is the speed of the can just before it hits the ground?

Another painter is standing on a ledge, with his hands a distance 3.75 m above the can when it falls off. He has lightning-fast reflexes and if the can passes in front of him, he can catch it. Does he get the chance?

Explanation / Answer

initial velocity = voy

acceleration ay = -g= -9.8 m/s^2

displacement y = -h = -15.9 m

time = t = 3.26 s

from equations of motion

y = voy*t + 0.5*ay*t^2

-15.9 = voy*3.26 - (0.5*9.8*3.26^2)

voy = 11.1 m/s

from equation of motion

vy = voy + ay*t

vy = 11.1 - (9.8*3.26)

vy = -20.848 m/s

speed = vy = 20.848 m/s <<----------answer

+++++++++++

along vertical

maximum height H = voy^2/2g = (11.1^2)/(2*9.8) = 6.28 m

6.28 > 3.75 m

so he gets the chance to catch the can

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