Answer to Question #165865 in Algorithms for Khidr

Question

A particle of mass M1 moving with initial velocity  is incident on a stationary particle of mass M2.After collision, M1 was deflected through an angle  and M 2 an angle .If the velocity of the particles after collision were  and  respectively.Show that for an elastic collision;

(a)    = 2

(b)   =2 +

(c)    =

Answer 1

Given,

Masses of the particles are $M_1$ and $M_2$ and their respective velocities after the collision are $v_1$ and $v_2$ and initial velocity of the mass $M_1$ is $v_o$

Let after the collision the deflection angle be $\theta$ for both,

Now, applying the conservation of linear momentum,

$\Rightarrow M_1v_0=M_1v_1\cos{\theta}+M_2v_2\cos{\theta}$

$\Rightarrow M_1v_1\sin{\theta}=M_2v_2\sin{\theta}$

Now, substituting the values,

$\Rightarrow M_1v_0=2M_2v_2\cos{\theta}$

Now, again,

$v_2=\frac{M_1v_0}{2M_2\cos{\theta}}$