Chapter 27 : Collision of Elastic Bodies 569
27.11. INDIRECT IMPACT OF A BODY WITH A FIXED PLANE
Fig. 27.6.
Consider a body having an indirect impact on a fixed plane as shown in Fig. 27.6.
Let u = Initial velocity of the body,
v = Final velocity of the body,
α = Angle, which the initial velocity of the body makes with the line of impact,
θ = Angle which the final velocity of the body makes with the line
of impact, and
e = Coefficient of restitution.
A little consideration will show, that the component of u, along the line of impact will cause the
direct ‘impact’ of the body with the fixed plane. The other component of u (i.e. along the perpendicu-
lar to the line of impact) will not affect the phenomenon of impact and will be equal to the other
component of v (i.e., along the perpendicular to the line of impact).
We know that velocity of approach
= u cos αand velocity of separation = v cos θ
The Newton’s Law of Collision of Elastic Bodies also holds good for this impact i.e.,
v cos θ = eu cos α
Notes : 1. In this impact also, we do not apply the principle of momentum (i.e. equating the
initial momentum and the final momentum) since the fixed plane has infinite mass.
- The components of initial and final velocities at right angles to the line of impact are same i.e.
u sin α = v sin θ
Example 27.11. A ball, moving with a velocity of 4 m/s, impinges on a fixed plane at an
angle of 30°. If the coefficient of restitution is 0.5, find,
(a) direction of the body after impact, and
(b) velocity of the body after impact.
Solution. Given : Initial velocity of the body (u) = 4 m/s ; Angle, which the initial velocity of
the body makes with the line of impact (α) = 90° – 30° = 60° and coefficient of restitution (e) =
0.5.