Question

A warning system has calculated that two asteroids will collide not far from Earth any time soon.

The smaller asteroid has the mass m and moves with the velocity vm. The bigger asteroid has the

mass M = 3m and the velocity of vM =

1

2

vm. They collide at an angle of α = 60◦ and turn into a

single heavy asteroid (inelastic collision):

M

m

α

β

(a) Calculate the velocity of the single object aer the collision.

(b) Determine the angle β aer the collision.​

Answer 1

Answer:

Explanation:

From the conservation of momentum:

(m+3m)Vcos β = 3m(0.5vm)+mvm cos60°

(m+3m)Vsinβ= mvm sin60°

Thus,

​(4mVcosβ)²

+ ​(4mVsinβ)²  = (2mvm)² + (mvm sin60°)²

= 16V² = v²m (4+3/4)

a) √19/8 vm

b) 4m √19/8 vm Sinβ = mvm sin60°

= Sinβ = 2/√19sin60 = √3/19

= β = arcsin √3/19  

= 23.41