You attach a meter stick to an oak tree, such that the top of the meter stick is

Question

You attach a meter stick to an oak tree, such that the top of the meter stick is 2.27 meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes 0.306 seconds to pass the length of the meter stick, how high above the ground was the acorn before it fell (assuming that the acorn didn't run into any branches or leaves on the way down)?

At the bottom of the meter stick, at the 0.306 second mark, I have a distance of 1.4994m travelled.
Since the top of the meter stick is 2.27m from the ground, i have the height being 0.4994 + 2.27m = 2.7694m. This is wrong though.

Explanation / Answer

let the height be h

time to cross the meter stick=0.306 s

let the velocity at the top of meter stick=u

and at the bottom=v

v=u+g*0.306

and v^2=u^2+2*g*1

put g=9.81

and solving for u and v we get

u=1.77 m/s and v=4.77 m/s

height of the top of meter stick from ground=2.27 m

then distance between top of meter stick and tree top=h-2.27

1.77^2=0^2+2*9.81*(h-2.27)

h=2.93 m

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