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Chapter 11: Q. 21 (page 288)

Fred (mass 60kg) is running with the football at a speed of 6.0m/swhen he is met head-on by Brutus (mass 120kg), who is moving at 4.0m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30.

Short Answer

Expert verified

They slide 7.6cmdistance in the direction of Brutus motion.

Step by step solution

01

Given information

We have given,

Fred mass =60kg

Fred speed =6m/s

Brutus mass =120kg

Speed =4m/s

coefficient of kinetic friction =0.3

We have to find how far they slide and which way.

02

Simplify

In an Collison the momentum will be always conserved. then,

PI=PF

Where the momentum is given by,

P=mv

Then,

m1v1+m2v2=(m1+m2)VV=m1v1+m2v2m1+m2V=60kg脳-6m/s+120kg脳4m/s60kg+120kgV=0.67m/s

This positive sign is indicates that the motion will be in BRUTUS side.

03

Simplify

Now we have to find the distance of slide.

The force after Collison will be equal to the force of friction.

Fnet=fk(m1+m2)a=-渭k(m1+m2)ga=-渭kga=-0.3脳9.8m/s2a=-2.94m/s2

Then using the equation of kinematics.

v22=v12+2ass=v22-v122as=0-(0.67)2-2脳2.94s=7.6cm

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