Question

You are out on an early morning jog when you see a family of squirrels in a tree that lies directly in your path. A squirrel on a branch 20 m high in the tree drops an acorn directly above your head as you run with speed 1.5 m/s beneath the squirrel's position. How far behind you does the acorn hit the ground?

Answer 1

The acorn hit the ground 3 m far away from me.

Explanation:

Here ,

time taken by the acorn to fall be 't',

Height of the tree is 20m ,

so
`S= 20m`

Acceleration due to gravity is -
`a=9.8(m)/(s^2)\approx 10 (m)/(s^2)`

Initial velocity is 0 ,so u=0

According to the second equation of motion ,

`s=ut+(1)/(2) at^2`

`20=(1)/(2) *10* t^2`

`t^2=4`

`t=2`sec.

Distance travelled by you in 2 sec

`\text{Distance} = \text{Speed} * \text{Time}`

Put speed= 1.5m/s² and time = 2sec

`Distance= 1.5 * 2\\Distance=3m`

Hence , the acorn hit the ground 3m far away from me.