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According to the U.S. Forest Service ("Limber Pine Dwarf Mistletoe", Forest Insect and Disease Leaflet 171, 1999), dwarf mistletoe is a parasitic plant that grows on the branches of pine trees. The mistletoe extracts its water and nutrients directly from the tree. One rare aspect of dwarf mistletoe is its seed dispersal mechanism. Rather than relying on birds or wind to spread seeds from pine tree to pine tree, mature mistletoe fruit literally explodes (as a result of extreme water pressure within the fruit). The explosion hurles the seed away from the pine tree. The seeds are coated with a sticky substance which causes them to adhere to whatever they hit. Ideally, the seed hits another nearby pine tree and begins to sprout.

The seed dispersal mechanism has been studied by T.E. Hinds and F.G. Hawksworth ( Science, Vol. 148, No. 3669 (Apr. 23 1965), pp. 517-519) by means of high-speed photography. They find that Arceuthobium cyanocarpum (the variety shown in the picture above) ejects is seeds with a speed of about 2100 cm/s.

Suppose that a certain dwarf mistletoe fruit expels a seed with a velocity of 2100 cm/s directed at 30° above the horizontal. Suppose further that the seed hits another tree at exactly the same height that it was launched from. Neglecting air resistance (note: neglecting air resistance is a poor assumption in this case) how far horizontally is the landing site displaced from the launch site?

System: The seed is treated as a point particle.

Models: Projectile motion, assuming One-Dimensional Motion with Constant Velocity in the horizontal direction and One-Dimensional Motion with Constant Acceleration in the vertical direction.

Approach: We first sketch the situation and define a coordinate system.

PICTURE

We choose the launch point to have the coordinates x = 0 m, y = 0 m and we choose to make t = 0 s at the instant of launch. Thus, we have the givens: