Answer:
Magnitude of velocity = 6.098 m/s and the angle at which system moves after collision is [tex]49.185^{o}[/tex]
Explanation:
Given:
mass of object 1 m1 = 11.0 kg
initial momentum of object 1, p1 = 50 kg-m/s
mass of object 2 m2 = 9.5 kg
initial momentum of object 2, p2 = 75 kg-m/s
We know that according to law of conservation of momentum, sum of initial momentum is equal to final momentum after collision. Aslo since the objects stick together the velocity v is same, Hence we get
p1 + p2 = (m1 + m2) x v
substituting the known values
50 + 75 = (11 + 9.5) x v
125 = 20.5 x v
v = 6.098 m/s
To find the direction of velocity:
The mass m1 moving towards south and mass m2 moving towards east, hence after collision both masses travel in south-west direction. In order to find angle Θ (refer image), we use
tan Θ = [tex]\frac{p_{1,collison} }{p_{2,collision} }[/tex] where, [tex]p_{1, collision}[/tex] and [tex]p_{2, collision}[/tex] are momentum values after collision.
[tex]p_{1, collision}[/tex] = m1 x v = 11 x 6.098 = 67.078 kg.m/s
[tex]p_{2, collision}[/tex] = m2 x v = 9.5 x 6.098 = 57.931 kg m/s
Hence,
tan Θ = [tex]\frac{67.078}{57.931}[/tex]
Θ = [tex]tan^{-1}[/tex] (1.1579)
