At a county fair, two children ram each other head-on while riding on the bumper

Question

At a county fair, two children ram each other head-on while riding on the bumper cars. Jill and her car, traveling left at 2.80m/s , have a total mass of 335kg . Jack and his car, traveling to the right at 2.20m/s , have a total mass of 250kg

Part A

Assuming the collision to be elastic, determine the speed of Jill and her car after the collision?

Part B

Determine the direction of the velocity of Jill and her car after the collision.

Part C

Determine the speed of Jack and his car after the collision.

Part D

Determine the direction of the velocity of Jack and his car after the collision.

Explanation / Answer

Consider two carsted by subscripts 1 and 2. Let m1 and m2 be the masses, u2 and u2 the velocities before collision, and v1 and v2 the velocities after collision.

The conservation of the total momentum demands that the total momentum before the collision is the same as the total momentum after the collision, and is expressed by the equation

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

Likewise, the conservation of the total kinetic energy is expressed by the equation

(m1*u1^2)/2 + (m*u2^2)/2 = (m1*v1^2)/2 + (m2*v2^2)/2

solving gives

v1 = (u1*(m1-m2) + 2*m2*u2)/(m1 + m2)

v2 = (u2*(m2-m1) + 2*m1*u1)/(m1 + m2)

u1 = 2.8 m/s ; m1 = 335 kg

u2 = -2.2 m/s ; m2 = 250 kg

v1 = -1.473 m/s

v2 = 3.5265 m/s

speed of car of jill after collision = v1 = -1.475

B) direction of velocity of jill's car after collision is towards right (negative velocity is taken to be towards right in this problem)

c)speed of Jack and his car after the collision = v2 = 3.5265 m/s

d)the direction of the velocity of Jack and his car after the collision is towards left(positive velocity is taken to be towards left in this problem)

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