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Step2247 [10]
3 years ago
7

In a Broadway performance, an 85.0-kg actor swings from a R = 3.90-m-long cable that is horizontal when he starts. At the bottom

of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?
Physics
1 answer:
Lera25 [3.4K]3 years ago
5 0

To solve this problem it is necessary to apply the concepts related to the conservation of the moment and the conservation of energy.

The conservation of energy implies that potential energy is transformed into kinetic energy or vice versa, depending on the process, in this way

KE = PE

\frac{1}{2}mv^2 = mgh

Where,

m = mass

v = velocity

h = height

g = gravitational acceleration

Re-arrange to find v,

\frac{1}{2}mv^2 = mgh

\frac{1}{2}v^2 = gh

v = \sqrt{2gh_1}

Replacing with our values we have that

v = \sqrt{2gh_1}

v = \sqrt{2(9.8)(3.9)}

v = 8.74m/s

At this point we can find the final speed through the conservation of the momentum, that is

mv = (m+M)V

Here,

m = mass of the first person

M = Mass of the second person

v = Initial velocity

V = Final Velocity

Replacing,

mv = (m+M)V

(85)(8.74) = (85+55)V

V = \frac{(85)(8.74) }{(85+55)}

V = 5.30m/s

Applying energy conservation again, but in this case using the values of the final state we have to

\frac{1}{2}(m+M)V^2 = (m+M)gh_2

\frac{1}{2}V^2 = gh_2

h_2 = \frac{V^2}{2g}

h_2 = \frac{5.3^2}{2*9.8}

h_2 = 1.433m

Therefore the maximum height that they reach after their upward swing is 1.433m

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