mass of carbon = m1
mass of unknown = m2
before collision
speed of m1 , v1i = 110 km/h
speed of m2 , v2i = -400 km/h
after collision
speed of m1 , v1if = -145 km/h
speed of m2 , v2f = 0 km/h
from momentum conservation
initial momentum before collision
Pi = m1*v1i + m2*v2i
after collision final momentum
Pf = m1*v1f + m2*v2f
from momentum conservation
total momentum is conserved
Pf = Pi
m1*v1i + m2*v2i = m1*v1f + m2*v2f .....(1)
from energy conservation
total kinetic energy before collision = total kinetic
energy after collision
KEi = 0.5*m1*v1i^2 + 0.5*m2*v2i^2
KEf = 0.5*m1*v1f^2 + 0.5*m2*v2f^2
KEi = KEf
0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2
.....(2)
solving 1&2
we get
v1f = ((m1-m2)*v1i - (2*m2*v2i))/(m1+m2)
-145 = ((m1 - m2)*110 - (2*m2*400))/(m1 + m2)
-145*m1 - 145*m2 = 110*m1 - 110*m2 - 800*m2
m1*(110 + 145 ) = m2*(800 - 145 + 110)
m1/m2 = 3 <<<-----ANSWER
v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)
v2f = (-(m2-3m2)*400 +(2*3m2*110))/(3m2 + m2)
v2f = (800 + 660)/4
v2f = 365 km/h <<----------ANSWER
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