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

Answer:

h = 51.5 m

Explanation:

Rate of increase of height of the tree is given as

$\frac{dh}{dt} = 1 m/year$

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

$H = H_o + 50\frac{dh}{dt}$

$H = 3 + 50(1)$

$H = 53 m$

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

$h = 50 + 1.5 = 51.5 m$