a. In order to find the speed of the paint can just before it hits the ground, we can use the equation:
v_f = v_i + a*t
where v_f is the final velocity, v_i is the initial velocity (0 m/s in this case, since the can is moving upward with the same speed as the scaffolding), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken for the fall (3.25 seconds).
v_f = 0 + (-9.8) * 3.25
v_f = -31.85 m/s
The speed of the can just before it hits the ground is 31.85 m/s downward.
b. To find out if the other painter has a chance to catch the can, we first need to find the distance the can falls during the time he has to react. We will assume the painter has an instant reaction time.
We can use the equation:
h = v_i * t + 0.5 * a * t^2
where h is the distance fallen, v_i is the initial velocity, a is the acceleration, and t is the time taken.
h = 0 * 3.25 + 0.5 * (-9.8) * 3.25^2
h = -51.53 m
Since the distance the paint can falls (-51.53 m) is greater than the height of the other painter's hands (4 m above the can when it falls off, so 15 + 4 = 19 m), it will pass in front of him, giving him a chance to catch it.
The Falling Paint Can: A painter is standing on scaffolding that is raised at a constant speed vi. As he travels upward he accidentally nudges a paint can off the scaffolding and it falls 15m to the ground. You are watching and measure with your stopwatch that it takes 3.25s for the can to reach the ground.
a.What is the speed of the can just before it hits the ground?
b.Another painter is standing on the ledge, which his hands 4m above the can when it falls off. He has lightning fast reflexes and if the paint can passes in front of him, he can catch it. Does he get the chance?
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