More from Jung about trees: "Taken on average, the commonest associations to its meaning are growth, life, unfolding of form in a physical and spiritual sense, development, growth from below upwards and from above downwards, the maternal aspect (protection, shade, shelter, nourishing fruits, source of life, solidity, permanence, firm-rootedness, but also being 'rooted to the spot'), old age, personality, and finally death and rebirth." Jung, Carl. Alchemical Studies from the Collected Works of C.G. Jung, Volume 13. Princeton: 1967. Print.
The tree, as stated above, has a broad range of meanings. I like to break it down into three parts: roots, body/trunk, and branches. They all serve a purpose and have great metaphorical meaning. Most simply the roots are the unconscious, the trunk - the ego, and the branches are the spirit.
In the case of this dream the tree is a cause for the grounding of a fast flying plane. I have to add the airplane into the interpretation along with the tree taking over my friend. When Apollo chased Daphne through the wood and he gained on her she asked her father, Peneus, to help her. He changed her into a laurel tree, to Apollo's dismay. Perhaps Martin becoming a tree was a needed change in order to ground the plane, albeit a tragedy. The plane landed safely, but Martin was lost. A sacrifice has been made here.