Chapter 27 : Collision of Elastic Bodies 563
27.9. INDIRECT IMPACT OF TWO BODIES
If the two bodies, before impact, are not moving along the line of impact, the collision is
called an indirect (or oblique) impact as shown in Fig. 27.3.
Fig. 27.3. Indirect impact.
Consider two bodies A and B having an indirect impact as shown in Fig. 27.3.
Let m 1 = Mass of the first body,
u 1 = Initial velocity of the first body,
α 1 = Angle which the initial velocity of the first body, makes with
the line of impact,
v 1 = Final velocity of the first body,
θ 1 = Angle, which the final velocity of the first body, makes with
the line of impact, and
m 2 , u 2 , α 2 , v 2 , θ 2 = Corresponding values for the second body,
A little consideration will show, that the components of u 1 , u 2 , v 1 and v 2 along the line of
impact, will cause the direct impact and all the relations for direct impact, will hold good for these
components. The other components of u 1 , u 2 , v 1 and v 2 , (i.e., along the perpendicular to the line of
impact) will not effect the phenomenon of impact in any way, and the component of initial velocity
will be equal to the component of final velocity of body.
Now u 1 cos α 1 = Component of the initial velocity of the first body along the
line of impact.
Similarly, u 2 cos α 2 = Component of initial velocity of the second body along the
line of impact.
v 1 cos θ 1 = Component of the final velocity of the first body along the line
of impact.
and v 2 cos θ 2 = Component of the final velocity of the second body along the
line of impact.
Now the law of conservation of momentum may be applied in the amended form in this case
also. i.e.,
Total initial momentum along the line of impact
= Total final momentum along the line of impact
m 1 u 1 cos α 1 + m 2 u 2 cos α 2
= m 1 v 1 cos θ 1 + m 2 v 2 cos θ 2