Question

A 2100 kg truck is traveling east through an intersection at 2.0m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling north at 5.0m/s. The other is a 1500 kg midsize traveling east at 10m/s. The three vehicles become entangled and slide as one body.
a. What is their speed just after the collision?
b. What is their direction just after the collision?

Answer 1

Answer:

a) Vf = 4.19m/s

b) α = 17.35° due north of east

Explanation:

By conservation of the linear momentum:

On the x-axis:

mt*Vt+m2*V2 = (mt + m1 + m2 )* Vfx

Vfx = 4 m/s

On the y-axis:

m1*V1 = (mt + m1 + m2) * Vfy

Vfy = 1.25 m/s

The speed is therefore:

$Vf = \sqrt{4^2+1.25^2}$

Vf = 4.19m/s

The angle of their velocity:

$\alpha = atan(\frac{1.25}{4})$

$\alpha = 17.35\°$