Question

what is the maximum height a 100 - w engine can lift a 100 - kg man in 3.00 minutes?
10.0 m
18.4 m
36.8 m
9.80 m

Explanation:

Step1: Calculate work done by engine

Power formula \(P=\frac{W}{t}\), so \(W = P\times t\). Given \(P = 100\space W\), \(t=3\times60 = 180\space s\). Then \(W=100\times180=18000\space J\)

Step2: Relate work to gravitational potential energy

Work done \(W = mgh\) (where \(m = 100\space kg\), \(g = 9.8\space m/s^{2}\)). Solving for \(h\), \(h=\frac{W}{mg}\). Substitute \(W = 18000\space J\), \(m = 100\space kg\), \(g=9.8\space m/s^{2}\). \(h=\frac{18000}{100\times9.8}\approx18.4\space m\)

Answer:

18.4 m