A ball is dropped onto a pad and rebounds with a velocity Vo at an angle of 60degree with the horizontal as shown in the picture. The ball will enter into the gap if Vo =?
Answers
Answer:
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Explanation:
The ball strikes the inclined plane (Ox) at point O (origin) with velocity v
0
=
2gh
........ (1)
As the ball elastically rebounds, it recalls with same velocity v
0
, at the same angle α from the normal or y axis (figure shown below). Let the ball strikes the incline second time at P, which is at a distance l (say) from the point O, along the incline. From the equation
y=v
0y
t+
2
1
w
y
t
2
0=v
0
cosατ−
2
1
gcosατ
2
where τ is the time of motion of ball in air while moving from O to P.
As τ
=0, so, τ=
g
2v
0
................. (2)
Now from the equation.
x=v
0x
t+
2
1
w
x
t
2
l=v
0
sinατ+
2
1
gsinατ
2
so, l=v
0
sinα(
g
2v
0
)+
2
1
gsinα(
g
2v
0
)
2
=
g
4v
0
2
sinα
(using 2)
Hence, the sought distance, l=
g
4(2gh)sinα
=8hsinα (Using equation 1)