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
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,
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:
And so now we can find the total distance they cover while sliding, using the equation
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,