4. Calculate the power used by a 40 kg man if he climbs a 6 m tall ladder in 15 seconds.

To calculate the power used, we need to determine the work done and then divide it by the time taken.<br /><br />First, let's calculate the work done. Work is given by the formula:<br />\[ \text{Work} = \text{Force} \times \text{Distance} \]<br /><br />The force here is the weight of the man, which can be calculated using:<br />\[ \text{Force} = \text{mass} \times \text{gravitational acceleration} \]<br />\[ \text{Force} = 40 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]<br />\[ \text{Force} = 392 \, \text{N} \]<br /><br />Now, the distance climbed is 6 meters. So, the work done is:<br />\[ \text{Work} = 392 \, \text{N} \times 6 \, \text{m} \]<br />\[ \text{Work} = 2352 \, \text{J} \]<br /><br />Next, we calculate the power used. Power is given by the formula:<br />\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]<br />\[ \text{Power} = \frac{2352 \, \text{J}}{15 \, \text{s}} \]<br />\[ \text{Power} = 156.8 \, \text{W} \]<br /><br />Therefore, the power used by the man is \( 156.8 \, \text{W} \).