Answer:
a
[tex]v = 1.9267 \ m/s[/tex]
b
The value is [tex]\mu = 0.0063[/tex]
Explanation:
From the question we are told that
The mass of the person is [tex]m_1 = 50.3 \ kg[/tex]
The horizontal velocity is [tex]u_1 = 2.44 \ m/s[/tex]
The mass of the shed is [tex]m_2 = 13.4 \ kg[/tex]
The distance covered is [tex]d = 30 \ m[/tex]
Generally from the law of momentum conservation we have that
[tex]m_1 * u_1 + m_2 * u_2 = (m_1 + m_2)v[/tex]
Here [tex]u_2[/tex] is the initial velocity of the shed which is 0 m/s
[tex]50.3 * 2.44 + 13.4 * 0 = (50.3 + 13.4) v[/tex]
=> [tex]v = 1.9267 \ m/s[/tex]
Generally the workdone by friction is mathematically represented as
[tex]W = \Delta KE[/tex]
[tex]W = \frac{1}{2} * m * (v_f - v )[/tex]
Here [tex]v_f[/tex] is the final velocity of the person and the shed when they come to rest and the value is [tex]v_f = 0 \ m/s[/tex]
Generally this workdone by friction is also mathematically represented as
[tex]W = - \mu * m * g * d[/tex]
=> [tex]- \mu * m * g * d = \frac{1}{2} * m * (v_f - v )[/tex]
=> [tex]\mu = - \frac{0.5 * ( v_f^2 - v^2 )}{g * d }[/tex]
=> [tex]\mu =- \frac{0.5 * ( 0^2 - 1.9267^2 )}{9.8 * 30 }[/tex]
=> [tex]\mu = 0.0063[/tex]
