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# Math work

Question No:1

First mass = m1

Velocity of first mass = v1

Angle below the x axis = θ

Second mass = m2

Velocity of second mass = v2

Angle above x axis = θ

a ) Initial momentum in x direction:

pix = mV1x

p2x = m2 V2x

b)

p I y = m1 V I y

p 2 y = m2 V 2 y

c)

pix  + p2x  = p I y + p 2 y

m1 V1x   + m2 V 2 y = m1 V I y   + m2 V 2 y

Pix  =  P f x

m1 v1x = (m1 + m2) vf   Cos θ

Piy  =  P f y

m2 v2iy = (m1 + m2 ) vf  Sin θ

=

= tan θ

Tan-1 () = θ

= 30

Vf =

Vf =

V = 2.886

d)

f x t =  m1 V1x   + m2 V2x

e)

f x t = m2 V2y   +   m2 V 2 y

Question No: 2

Mass of truck = m1 = 2000kg

Mass of car = 1200 kg

Angle after accident = 51.34

Coefficient of friction = µ = 0.8

Initial speeds of truck and car = ?

Kinetic energy of the system is given as = ½ mvf – ½ mvi2

F =  µN

N= ( m1 + m2 )g

N = (2000 + 1200)9.8

=31360

F =  µN

F = 0.8 x 31360

=25088

Final velocity of truck

25800 = ½ mvf2 – ½ mvi2

2 x 25800/ 2000 = Vf 2  –  V i2

25.8 = Vf 2  –  V i2

Vf2  + Vi2  = 2g d

= 2 x 9.8  x 9.18

=179.928

2 Vi2   = 179.928 – 25.8

Initial velocity of truck =10.14 m/sec

Vf =

Vf =

= 8.630

m1 vix = (m1 + m2) vf   Cos θ

vi = (3200) 8.06 cos (51.34) /1200

v1 = 10.23 