A car is approaching a truck moving in the same direction on a one lane straight

Question

A car is approaching a truck moving in the same direction on a one lane straight road. The car driver looks at his cellphone momentarily (II) and misjudges the distance resulting in a collision. The cars don't stick together after the collision, the front end of the car is dented during the collision however. The car's mass is 1200 kg and it was moving with a velocity of 25.0 m/s {+i} before the collision, and the truck's mass and speed were 9000 kg and 20.0 m/s {+i} respectively. If the car's velocity drops to 18.0 m/s {+i} momentarily, what is the velocity of the truck just after the collision? How much Energy is lost to the deformation of the car's front end? Calculate the Impulse (magnitude and direction) that the car experiences during the collision.

Explanation / Answer

Let

m1 = 1200 kg, u1 = 25 m/s

m2 = 9000 kg, u2 = 20 m/s

after the collsion,

v1 = 18 m/s

a) Apply conservation of momentum

m1*u1 + m2*u2 = m1*v1 + m2*v2

v2 = (m1*u1 + m2*u2 - m1*v1)/m2

= (1200*25 + 9000*20 - 1200*18)/9000

= 20.93 m/s <<<<<<---------Answer

b) Energy lost = Ki - Kf

= (0.5*m1*u1^2 + 0.5*m2*u2^2) - (0.5*m1*v1^2 + 0.5*m2*v2^2)

= (0.5*1200*25^2 + 0.5*9000*20^2) - (0.5*1200*18^2 + 0.5*9000*20.93^2)

= 9308 J <<<<<<---------Answer

c) Impulse = change in momentum of truck

= m2*(v2 - u2)

= 9000*(20.93 - 20)

= 8400 N.s <<<<<<---------Answer

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