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EdtVew History Bookmarks People Window Help https://s bemView?assi P100AFL15 Signad in as fozad ardagh Helo previous 1 of 10 ne Part A The figures below show brds-eye viows of six automobile crashes an ihstant boore they ooour. The audomobiles have dierent masses and incoming velooiies as shown. After impact, the automobles remain joined together and skid to nest in the direction shown by thisal Rank these crashes according to the angie 8, countarclockwise as shown, at which to wreckage initaly skids Rank from largest to smallest. To rank items as equivalent, overlap them 0 m's 0o0 kg 00 kg l0 m/ 700 k 1000 kg 1500 k 1000 kg MacBook Pro 8 command option

Explanation / Answer

m1 = 1200 kg

m2 = 700 kg

before collision

u1x = 9 m/s               u2y = 15 m/s

after collision m1 , m2 combine and move with speed V1

fom momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V1x

1200*9 = (1200+700)*v1x

V1x = 5.68 m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v1y

0 + 700*15 = (1200+700)*v1y

v1y = 5.53 m/s

theta1 = arctan(v1y/v1x) = arctan(5.53/5.68)

theta 1 = 44.23

--------------------------------------

m1 = 700 kg

m2 = 700 kg

before collision

u1x = 7 m/s               u2y = 7 m/s

after collision m1 , m2 combine and move with speed V2

fom momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V2x

700*7 = (700+700)*v2x

V2x = 3.5 m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v2y

0 + 700*7 = (700+700)*v2y

v2y = 3.5 m/s

theta2 = arctan(v1y/v1x) = arctan(3.5/3.5)

theta 2 = 45

--------------------------------------

m1 = 1000 kg

m2 = 1000 kg

before collision

u1x = 10 m/s               u2y = 7 m/s

after collision m1 , m2 combine and move with speed V3

fom momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V3x

1000*10 = (1000+1000)*v3x

V3x = 5 m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v3y

0 + 1000*7 = (1000+1000)*v3y

v3y = 3.5 m/s

theta3 = arctan(v3y/v3x) = arctan(3.5/5)

theta 3 = 35

--------------------------------------

m1 = 1000 kg

m2 = 1500 kg

before collision

u1x = 15 m/s               u2y = 10 m/s

after collision m1 , m2 combine and move with speed V4

fom momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V4x

V4x = m1*u1x/(m1+m2) m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v4y

v4y = m2*u2y/(m1+m2) m/s

theta4 = arctan(v4y/v4x) = arctan((m1*u2y)/(m1*u1x))

theta 4 = arctan(1000*10/(1000*15))

theta4 = 33.7

--------------------------------------

m1 = 1000 kg                 m2 = 1000 kg

before collision

u1x = 7 m/s               u2y = 10 m/s

after collision m1 , m2 combine and move with speed V5

fom momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V5x

V5x = m1*u1x/(m1+m2) m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v5y

v5y = m2*u2y/(m1+m2) m/s

theta5 = arctan(v4y/v4x) = arctan((m1*u2y)/(m1*u1x))

theta 4 = arctan(1000*10/(1000*7))

theta4 = 55

------------------------

m1 = 1000 kg

m2 = 1000 kg

before collision

u1x = 10 m/s               u2y = 10 m/s

after collision m1 , m2 combine and move with speed V6

from momentum conservation

initial momentum = final momentum

along x

m1*u1x + m2*u2x = (m1+m2)*V6x

V6x = (m1*u1x)/(m1+m2) m/s

along y

m1*u1y + m2*u2y = (m1+m2)*v6y

V6y = (m1*u2y)/(m1+m2)

theta6 = arctan(v6y/v6x) = arctan(10/10)

theta 6 = 45

--------------------------------------

5 > 2 = 6 > 1 > 3 > 4

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