Some plants disperse their seeds when the fruit splits and contracts, propelling the seeds through the air. The trajectory of these seeds can be determined with a high-speed camera. In an experiment on one type of plant, seeds are projected at 20 cm
above ground level with initial speeds between 2.3 m/s
and
4.6 m/s.
The launch angle is measured from the horizontal, with +90
corresponding to an initial velocity straight up and -90^circ
straight down.
If a seed is launched at an angle of 0
with the maximum
initial speed, how far from the plant will it land? Ignore air resistance,
and assume that the ground is flat.