You attach a meter stick to an oak tree, such that the top of the meter stick is 2.67 meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes 0.196 seconds to pass the length of the meter stick, how high above the ground was the acorn before it fell, assuming that the acorn did not run into any branches or leaves on the way down?

Question

You attach a meter stick to an oak tree, such that the top of the meter stick is  2.67  meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes  0.196  seconds to pass the length of the meter stick, how high above the ground was the acorn before it fell, assuming that the acorn did not run into any branches or leaves on the way down?

I got 7.71 and 5.53 but they both ended up wrong.

oobleck · Answer

You know that your answers are too big, because the average speed of the acorn is only 0.196 m/s. Now, in the first second, it falls 4.9m, right? And v = 9.8 m/s after 1 second. That's way too fast to have fallen either of your distances.

you know that if it takes t seconds to fall to the top of the stick, then
(t+0.196)^2 - t^2 = (2.67-1.67)/4.9
Now find h, since
h - 4.9t^2 = 2.67

I get h = 3.545