Question

You carve your and your sweetheart’s initials in the trunk of a 3-meter tall tree, 1.5 meters above the ground. Fifty years later you return, and on a romantic whim, you find your old carved heart. The tree has grown one meter taller per year. How high above ground are your initials?

Answer 1

h = 51.5 m

Step-by-step explanation:

Rate of increase of height of the tree is given as

`(dh)/(dt) = 1 m/year`

now we know that if tree height is increasing at above rate then the final height of the tree after 50 years will be given as

`H = H_o + 50(dh)/(dt)`

`H = 3 + 50(1)`

`H = 53 m`

now since this increase in height is from the root side

so the height of the romantic whim on the tree will be now 50 m high from its initial position

so new height will be

`h = 50 + 1.5 = 51.5 m`