Fred (mass 65 kg) is running with the football at a speed of 5.9 m/s when he is met head-on by brutus (mass 130 kg), who is moving at 4.4m/s. brutus grabs fred in a tight grip, and they fall to the ground. how far do they slide? the coefficient of kinetic friction between football uniforms and astroturf is 0.30.

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,