Answer :
Explanation:
It is given that,
Mass of actor, m₁ = 80 kg
Length of cable, h₁ = 3.75 m
Mass of costar, m₂ = 55 kg
Using the conservation of energy to find the speed of the performer at the bottom of the arc as :
Potential energy at start = kinetic energy at end
[tex]mgh_1=\dfrac{1}{2}mv_1^2[/tex]
[tex]v_1=\sqrt{2gh_1}[/tex]
[tex]v_1=\sqrt{2\times 9.8\times 3.75}[/tex]
[tex]v_1=8.57\ m/s[/tex]
Let v₂ is its speed after the collision. Now using the conservation of momentum as :
[tex]m_1v_1=(m_1+m_2)v_2[/tex]
[tex]v_2=\dfrac{m_1v_1}{(m_1+m_2)}[/tex]
[tex]v_2=\dfrac{80\times 8.57}{80+55}[/tex]
[tex]v_2=5.07\ m/s[/tex]
Let h₂ is the maximum height they reach after their upward swing. Again using the conservation of energy as :
[tex]\dfrac{1}{2}mv_2^2=mgh_2[/tex]
[tex]h_2=\dfrac{v_2^2}{2g}[/tex]
[tex]h_2=\dfrac{(5.07)^2}{2\times 9.8}[/tex]
[tex]h_2=1.31\ m[/tex]
Hence, this is the required solution.
The maximum height which it has to reach after their upward swing is:
- 1.31m
What is Maximum Height?
This refers to the highest vertical position which an object can reach starting from a rest point along an axis.
From the given set of data, we have
Mass of the actor, m₁ = 80 kg
Cable length, h₁ = 3.75 m
Mass of the costar, m₂ = 55 kg
We are using the conversion of energy:
Potential energy at start = kinetic energy at end
Therefore, v1 = 8.57 m/s
v2 = 5.07 m/s
Then to calculate for the maximum height, we would get:
1/2mv2= mgh2
h2= v²2/2g
h2= (5.07)²/2 x 9.8
h2= 1.31m.
This is the maximum height.
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