Question

current attempt in progress
in 1.77 minutes, a ski lift raises four skiers at constant speed to a height of 146 m. the average mass of each skier is 68.8 kg. what is the average power provided by the tension in the cable pulling the lift?
number i
units
save for later
attempts: 0 of 3 used
submit answer
using multiple attempts will impact your score.
20% score reduction after attempt 2

Explanation:

Step1: Calculate the total mass of skiers

The total mass \(m\) of four skiers is \(m = 4\times68.8\space kg=275.2\space kg\)

Step2: Calculate the work done

The work done \(W\) against gravity is \(W = mgh\), where \(g = 9.8\space m/s^{2}\) and \(h=146\space m\). So \(W=275.2\times9.8\times146\)

$$
LATEXBLOCK0
$$

Step3: Convert time to seconds

The time \(t = 1.77\space minutes\). Since \(1\space minute=60\space s\), \(t=1.77\times60 = 106.2\space s\)

Step4: Calculate the average power

The average power \(P=\frac{W}{t}\). Substitute \(W = 393255.36\space J\) and \(t = 106.2\space s\)

$$ P=\frac{393255.36}{106.2}=3703\space W $$

Answer:

\(3703\space W\)