A car of mass 1800000 g, going 150 km/h rear ends a truck, 5500 kg going 100000 m/h. What are their velocities after an elastic collision in one dimension?

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Answer:

v = 2099.5 km/h, v’ = -618.8 km/h

or

v =-1996.6 km/h, v’ = 721.7 km/h

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

For elastic,

mu+m’u’ = mv+m’v’………………… Equation 1

Total kinetic energy before collision is equal to total kinetic energy after collision

mu²+m’u’² = mv²+m’v’²…………. Equation 2

Where m and m’ are the mass of the car and truck respectively, and u and u’ are the initial velocity of the car and the truck respectively, v and v’ are the final velocity of the car and the truck respectively.

Given: m = 1800000 g = 1800 kg, m’ = 5500 kg, u = 150 km/h, u’ = 100000 km/h

Answer:v = 2099.5 km/h, v’ = -618.8 km/horv =-1996.6 km/h, v’ = 721.7 km/hExplanation:From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

For elastic,

mu+m’u’ = mv+m’v’………………… Equation 1

Total kinetic energy before collision is equal to total kinetic energy after collision

mu²+m’u’² = mv²+m’v’²…………. Equation 2

Where m and m’ are the mass of the car and truck respectively, and u and u’ are the initial velocity of the car and the truck respectively, v and v’ are the final velocity of the car and the truck respectively.

Given: m = 1800000 g = 1800 kg, m’ = 5500 kg, u = 150 km/h, u’ = 100000 km/h

Substitute these values into equation 1 and 2

1800(150)+5500(100000) = 1800v+5500v’

1800v+5500v’ = 375500………………. Equation 3

1800(150²) +5500(100000²) = 1800v²+5500v’²…………………. Equation 4

Solving equation 3 and 4 simultaneously,

v = 2099.5 km/h, v’ = -618.8 km/h

or

v =-1996.6 km/h, v’ = 721.7 km/h