Answer :
Final answer:
The speed at which a 4 kg bucket can be raised with a power output of 116 W is approximately 2.96 meters per second, calculated using the power formula P = mgv.
Explanation:
Given that the power output is 116 W, and the mass of the bucket and water is 4 kg, we seek to find the speed at which the bucket can be raised. We can use the relationship between power (P), work done (W), and time (t), which is expressed as P = W/t. To lift the bucket of water, work is done against gravity, and this work can be represented as W = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity (9.8 m/s2), and 'h' is height. Because power is also equal to the rate of doing work, we know that P = W/t = (mgh)/t. However, since speed (v) is equal to distance (h) divided by time (t), we can then express power as P = mgv. Solving for v, we get v = P/(mg) = 116 W / (4 kg \\* 9.8 m/s2) = 2.96 m/s.
Therefore, you can raise the bucket with a speed of approximately 2.96 meters per second.
