A ball of mass 100 grams hits the floor with a speed 10 m/s making an angle of incidence 30° with the normal. The speed of reflected ball and the angle of reflection is, (consider collision to be elastic)
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Explanation:
Velocity of approach in the given case is the normal component of velocity.
Hence, v
n
=vcosθ
By definition of coefficient of restitution, velocity of separation will be,
v
n
′
=ev
n
=evcosθ
Tangential component of velocity will not change.
v
t
′
=v
t
=vsinθ
Speed of reflected ball is:
v
′
=
v
n
2
+v
t
2
=
(evcosθ)
2
+(vsinθ)
2
=v
e
2
cos
2
θ+sin
2
θ
Angle with normal is given by:
θ
′
=tan
−1
v
n
′
v
t
′
θ
′
=tan
−1
(
evcosθ
vsinθ
)
θ
′
=tan
−1
(
e
tanθ
)
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