Question

Two cars approach an intersection at a right angle to each other.  If an inelastic collision occurs at the intersection, determine the x component of the final momentum of the combined vehicles.  Car 1 of mass 865 kg approaches the intersection from the left with a speed of 19.49 m/s.  Car 2 of mass 1,121.17 kg approaches the intersection from the south with a speed of 14.98 m/s.

Answer 1

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Two cars approach an intersection at a right angle to each other. If an inelastic collision occurs at the intersection, determine the angle of the combined vehicles after collision relative the x direction which is the direction that car 1 was traveling in before collision. Car 1 of mass 820.68 kg approaches the intersection from the left with a speed of 18.54 m/s. Car 2 of mass 868.68 kg approaches the intersection from the south with a speed of 20.18 m/s.   

A 3.40-kg ball, moving to the right at a velocity of +3.46 m/s on a frictionless table, collides head-on with a stationary 9.90-kg ball. Find the final velocities of (a) the 3.40-kg ball and of (b) the 9.90-kg ball if the collision is elastic. (c) Find the final velocity of the two balls if the collision is completely inelastic.






Let:
m1, m2 be the masses of the balls,
u1, u2 be their initial velocities,
v1, v2 be their final velocities.

For the elastic collision:
m1 u1 + m2 u2 = m1 v1 + m2 v2
u2 - u1 = - (v2 - v1)

As u2 = 0, these simplify to:
3.40 * 3.46 = 3.40v1 + 9.90v2 ...(1)
- 3.46 = v1 - v2 ...(2)

(a)
Multiplying (2) by 9.90 and adding (1):
(3.40 - 9.90)3.46 = (3.40 + 9.90)v1
v1 = - 1.69 m/s to 3 sig. fig.

(b)
From (2):
v2 = v1 + 3.46
= 1.77 m/s to 3 sig. fig.

(c)
For the inelastic collision:
m1 u1 + m2 u2 = m1 v1 + m2 v2
v1 = v2

As u2 = 0 and v2 = v1:
3.40 * 3.46 = (3.40 + 9.90)v1
v1 = v2 = 0.885 m/s to 3 sig. fig.