You are working on a field research project testing the hypothesis that acorns o

Question

You are working on a field research project testing the hypothesis that acorns on the lower branches of an oak tree fall to the ground earlier in the season than those on a trees upper branches. To test this hypothesis, you attach a meter stick to an oak tree, such that the top of the meter stick is 1.47 meters above the ground, and place a video camera and motion detector level with and pointing at the meter stick. When an acorn falls from somewhere higher up in the tree and passes between the camera and meter stick, a motion detector triggers the camera to take 3.15 s of film - capturing video of the acorn as it falls past the meter stick. The video is time stamped so you know what day and what time the acorn fell. Over the course of several months, the camera takes data from hundreds of falling acorns. When you go back to analyze the recorded video, you find that the first acorn falls straight down and takes 0.216 seconds to pass the length of the meter stick. From how high up in the tree (i.e., how far above the ground) was this first acorn before it fell?

Explanation / Answer

Here ,

let the initial speed of acorn when it is 1.47 m above ground is u

Now, t = 0.216 m

Using second equation of motion

d = u*t + 0.5 * gt^2

1.47 = u * 0.216 + 0.5 * 9.8 * 0.216^2

solving

u = 5.747 m/s

Now , Height from which it fall = 1.47 + u^2/(2 *g)

Height from which it fall = 1.47 + 5.747^2/(2 * 9.8)

Height from which it fall = 3.16 m

acron fell from 3.16 m above ground

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