A cherry falls from a tree branch that is 9 feet above the ground, how far above the ground is the cherry after 0.2 seconds?

a cherry falls from a tree branch that is 9 feet above the ground, how far above the ground is the cherry after 0.2 seconds?

1 Answer
Apr 15, 2018

8.36 feet

Explanation:

SUVAT equations

If the cherry is undergoing free fall with negligible air resistance we can assume that the only acceleration is acceleration due to gravity which is #9.81 ms^{-2}#

Assuming the cherry's height is the same as that of the tree branch it is 9 ft above the ground, or #2.74 m# in SI units.

#s=ut + 1/2at^2# can be used to find the displacement for a body with uniform acceleration.

Time #t=0.2s#
Acceleration #a=9.81 ms^{-2}#
Initial velocity #u=0#, since we assume the cherry isn't moving until it starts falling.
This gives us all the values we need to find the displacement #s#

#s=1/2 times (9.81) times (0.2)^2 = 0.1962 m# which is equal to #0.64# feet

Now, notice that this is the displacement from the branch, not distance from the ground. To find that we subtract the distance fallen from the height of the branch.

#9-0.64=8.36# feet