Determine the velocities of each vehicle immediately after the collision. Express these in vector form and calculate their respective magnitudes.

Question

Roundabouts are considered safer than typical cross-street intersections

since they greatly reduce the possibility of “T-bone” collisions, where one vehicle

impacts another at a right angle, resulting in greater injuries and damage.

Consider a collision that occurs on a roundabout, as shown. The masses of the vehicles

are mA = 1800 kg, and mB = 2200 kg. At the time of impact, the path of vehicle A makes

an angle of 79° with the line of impact at a velocity of V_A1= 11 m/s, and the path of vehicle B makes an angle of 53° with the line of impact with a velocity of V_B1 =7 m/s. The coefficient of restitution, e = 0.56.

Determine the velocities of each vehicle immediately after the collision. Express these

in vector form and calculate their respective magnitudes.

Answer 1

VA =VAx i^+VAy j^

V

B

=

V

B

x

i

^

+

V

B

y

j

^

VB =VBx i^+VBy j^

The magnitudes of these velocities can be found using:

∣

V

A

∣

=

V

A

x

2

+

V

A

y

2

∣VA ∣=VAx2 +VAy2

∣

V

B

∣

=

V

B

x

2

+

V

B

y

2

∣VB ∣=VBx2 +VBy2

Let me compute these values for you.

The velocities of each vehicle immediately after the collision are as follows:

1. Vehicle A:
2. Velocity in vector form: V
3. A
5. =
6. 3.91
7. i
8. ^
10. +
11. 10.80
12. j
13. ^
17. VA =3.91i^+10.80j^ m/s
18. Magnitude: ∣
19. V
20. A
22. ∣
23. =
24. 11.48
27. ∣VA ∣=11.48 m/s
28. Vehicle B:
29. Velocity in vector form: V
30. B
32. =
33. 2.73
34. i
35. ^
37. +
38. 5.59
39. j
40. ^
44. VB =2.73i^+5.59j^ m/s
45. Magnitude: ∣
46. V
47. B
49. ∣
50. =
51. 6.22

1. ∣VB ∣=6.22 m/s