Answer:
0.16 m
Explanation:
First, we have to find the combined velocity of Fred+Brutus after the collision. This can be done by using the law of conservation of momentum
[tex]p_i = p_f \\m_F u_F + m_B u_B = (m_F +m_B)v[/tex]
where
mF = 65 kg is the mass of Fred
mB = 130 kg is the mass of Brutus
uF = +5.9 m/s is the initial velocity of Fred
uB = -4.4 m/s is the initial velocity of Brutus
v is their final combined velocity
Solving for v,
[tex]v=\frac{m_F u_F + m_B u_B}{m_F+m_B}=\frac{(65 kg)(+5.9 m/s)+(130 kg)(-4.4 m/s)}{65 kg+130 kg}=-0.97 m/s[/tex]
and the negative sign means the direction is the one that Brutus had before the collision.
Now we can calculate the deceleration due to the frictional force on Fred+Brutus when they slide together:
[tex]a=-\mu g=-(0.30)(9.8 m/s^2)=-2.94 m/s^2[/tex]
And so now we can find the total distance they cover while sliding, using the equation
[tex]v^2 - u^2 = 2ad[/tex]
where
v = 0 is their final velocity
u = 0.97 m/s is their initial velocity
a = -2.94 m/s^2 is their acceleration
d is the distance covered
Solving for d,
[tex]d=\frac{v^2-u^2}{2a}=\frac{0-(0.97 m/s)^2}{2(-2.94 m/s^2)}=0.16 m[/tex]
