You are on a ladder painting your house. You accidentally drop a bucket of paint weighing 10lb from a height of 17ft. With what speed do the paint and bucket hit the rose bushes below? Would it be different if you dropped your paintbrush weighing 1/2 lb instead?

Question

You are on a ladder painting your house. You accidentally drop a bucket of paint weighing 10lb from a height of 17ft. With what speed do the paint and bucket hit the rose bushes below? Would it be different if you dropped your paintbrush weighing 1/2 lb instead?

b) what color is the paint?

Answer 1

To calculate the speed at which the paint and bucket hit the rose bushes, we can use the principle of conservation of energy. The potential energy gained by the falling object is converted into kinetic energy just before impact. We can equate the potential energy to the kinetic energy to find the speed.

1) Calculating the speed when the bucket of paint is dropped:
The potential energy (PE) gained by the bucket is equal to the product of its weight (W) and the height (h) from which it is dropped. Since the weight is given as 10 pounds and the height is 17 feet, we need to convert them to the metric system for calculations.
Weight (W) = 10 lb
Height (h) = 17 ft

Now, we convert the weight to kilograms (kg) and the height to meters (m) for consistent units:
Weight (W) = 10 lb × 0.4536 kg/lb = 4.536 kg
Height (h) = 17 ft × 0.3048 m/ft = 5.1824 m

Next, we equate the potential energy to the kinetic energy just before impact:
PE = KE
mgh = (1/2)mv^2

Where:
m = mass of the object (bucket of paint)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height from which the object is dropped
v = velocity/speed at impact

Simplifying the equation:
mgh = (1/2)mv^2
gh = (1/2)v^2
2gh = v^2
v^2 = 2gh
v = √(2gh)

Now we can plug in the values:
v = √(2 × 9.8 m/s^2 × 5.1824 m)
v ≈ 9.78 m/s

Therefore, the bucket of paint hits the rose bushes with a speed of approximately 9.78 m/s.

2) Calculating the speed when the paintbrush is dropped:
Using the same equation: v = √(2gh)
Now we will consider the weight of the paintbrush which is given as 1/2 lb.

Weight (W) = (1/2) lb × 0.4536 kg/lb = 0.227 kg
Height (h) = 17 ft × 0.3048 m/ft = 5.1824 m

Substituting these values into the equation:
v = √(2 × 9.8 m/s^2 × 5.1824 m)
v ≈ 9.78 m/s

Therefore, the paintbrush, despite weighing less, hits the rose bushes with the same speed of approximately 9.78 m/s.

b) The color of the paint is not mentioned in the question, so we cannot determine the color based on the given information.

You are on a ladder painting your house. You accidentally drop a bucket of paint weighing 10lb from a height of 17ft. With what speed do the paint and bucket hit the rose bushes below? Would it be different if you dropped your paintbrush weighing 1/2 lb instead?

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