The displacement is 127.99 meters.
The word displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Neglecting air drag, the launch angle for max range is 45 degrees so that the horizontal speed is
35*cos45 = 24.75 m/s
and the initial vertical speed is also 24.75 m/s
A kinematic equation provides the time in the air as
[tex]s = u*t +\frac{1}{2} a*t^2[/tex]
so
[tex]0 = 24.75*t - 0.5*9.81*t^2[/tex]
and t = 5.04587 secs (vertical component)
so the range to first bounce is
5.04587 x 24.75 = 124.88 m
A triangle of distances can now be drawn to clarify the new distance to the goal posts.
The cos rule provides the answer:
[tex]124.88^2 + 25^2 - 2*124.88*25*cos(130)[/tex]
[tex]= Displacement^2 = 16380.557[/tex]
Therefore,
The displacement is 127.99 meters.
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