Question

An apple falls (from rest) from a tree. It hits the ground at a speed of about 4.9 m/s. What is the approximate height (in meters) of the tree above the ground? The magnitude of the gravitational acceleration g = 9.8 m/s2 Enter your answer in meters. Keep 2 decimal places.

Answer 1

The inicial height of the apple is 1.22 meters

Step-by-step explanation:

Using the equation for conservarion of mechanical energy:

`E=V+K=constant`

`K_i=(1)/(2)mv_i^2` where v is the velocity

`V=mgh`where h is the height

We equate the initial mechanical energy to the final:

Since
`v_0=0\ and h_f=0`:

`(1)/(2)mv_0^2+mgh_0= (1)/(2)mv_f^2+mgh_f\\gh_0= (1)/(2)v_f^2`

Solving for h:

`h_0=(4.9^2)/(2g)= 1.22 m`