The time τ it takes the golf ball
to travel a horizontal distance d
is given by
d = x(τ)
= v0xτ
= v0 cos(θ)
τ
→
τ =
d / v0 cos(θ)
The vertical position of the golf ball
at the instant τ
is given by
yball(τ)
= v0yτ
- gτ2/2
= v0 sin(θ) d /
v0 cos(θ)
- gτ2/2
= d tan(θ)
- gτ2/2
= h
- gτ2/2
=
yobject(τ)
Hence, the ball hits the object at instant
τ.
The ball will always hit the object, independent of the initial velocity
(within some reasonable values of course).
The larger the initial velocity is, the higher the position where
the ball collides with the freely falling object.
This phenomenon is known as the
"The Monkey and the
Hunter" experiment.
Walter Lewin dresses himself as a hunter and the object in his
demonstration is a toy monkey.
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