Car of 1000kg going east at 25 m/s hits a kid of 2500 kg going east at 10 m/s. what is the velocity of car after collision if kid moved 15ms?

Ic = 1,000*25 = 25,000 kg*m/sec 

It = 2,500*10 = 25,000 kg*m/sec 

I = Ic+It = 50,000 kg*m/sec 

KEc = 25^2*1000/2 = 312,500 joule 

KEt = 10^2*2500 = 250,000 joule 

KE = 562,500 joule 

a)

Vt' = 15 m/sec

It' = 2,500*15 = 37,500 kg*m/sec 

Vc' = I-It')/mc = (50,000-37,500)/1000 = 12,5 m/sec 

KE' = 500*12.5^2+15^2*1,250 = 359,375 joule 

k = 100*(562,500-359,375)/562,500 = 36.11 %

b)

prior impact

I = 50,000 kg*m/sec 

KEc = 25^2*1000/2 = 312,500 joule

KEt = 10^2*2500 = 250,000 joule

KE = 562,500 joule 

after impact

both momentum and kinetic energy are  conserved

mc*Vc' + mt*Vt' = 50,000

mc*Vc'^2+mt*Vt'^2 = 1,125,000 joule 

Vc' = (50,000-mt*Vt')/1000

1000*((50,000-2500*Vt')/1000)^2+mt*Vt'^2 = 1,125,000

1000*(2,500+6.25Vt'^2-250Vt')+2500*Vt'^2 = 1,125,000

2,500,000+6,250Vt'^2-250,000Vt'+2,500*Vt'^2 = 1,125,000

8750Vt'^2-250,000Vt'+1375,000 = 0 

8.75Vt'^2-250Vt'+1375 = 0

Vt' = (250 ± √ 250^2-8.75*4*1375)/17.5 = 21.137 ; 7.435 m/sec

Vt' must be higher than Vt, therefore 21.137 value  will suit !!

50,000-21.137*2,500 = -2.842 kg*m/sec 

Vc' = -2.842/1000 = -2.842 m/sec 

KE'' = -2,842^2*1000+21,137^2*2500 = 1,125,000 joule...  no loss of energy at all

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