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problem reference 6.2
a hot air balloon lifts a 150 kg basket straight up by means of a rope. the basket has an upward acceleration of 1.20 m/s² and is lifted from rest a distance of 14.0 m.
what is the final speed of the person? use the work - energy method to solve.
8.75 m/s
33.3 m/s
2.12 m/s
5.77 m/s

Explanation:

Step1: Apply work - energy theorem

The work - energy theorem states that \(W_{net}=\Delta K = K_{f}-K_{i}\). The initial kinetic energy \(K_{i}=\frac{1}{2}mv_{i}^{2}\), since \(v_{i} = 0\) (starts from rest), \(K_{i}=0\). The net work \(W_{net}=F_{net}d\), and \(F_{net}=ma\). So \(W_{net}=mad\). The final kinetic energy \(K_{f}=\frac{1}{2}mv_{f}^{2}\).

Step2: Equate and solve for \(v_{f}\)

Set \(W_{net}=K_{f}\), then \(mad=\frac{1}{2}mv_{f}^{2}\). Cancel out the mass \(m\) (since \(m
eq0\)) from both sides of the equation. We get \(ad=\frac{1}{2}v_{f}^{2}\). Rearranging for \(v_{f}\), we have \(v_{f}=\sqrt{2ad}\).

Substitute \(a = 1.20\space m/s^{2}\) and \(d=14.0\space m\) into the formula:

$$
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$$

Answer:

\(5.77\space m/s\)