Question

4. Free Fall: An acorn falls from a tree and hits the ground with a speed of 10 m/s.From what height did the acorn fall?How long was the acorn in the air?

Answer 1

Given data:

* The initial speed of the acorn is 0 m/s.

* The final speed of the acorn is 10 m/s.

Solution:

(a). By the kinematics equation, the height of the acorn fall is,

$v^2-u^2=2gh$

where h is the height, u is the initial velocity, v is the final velocity, and g is the acceleration due to gravity,

Substituting the known values,

$\begin{gathered} 10^2-0=2\times9.8\times h \\ 100=19.6\times h \\ h=\frac{100}{19.6} \\ h=5.1\text{ m} \end{gathered}$

Thus, the height of the acorn fall is 5.1 m.

(b). By the kinematics equation, the time taken by the acorn to reach the ground is,

$v-u=gt$

where t is the time taken by the acorn to reach the ground,

Substituting the known values,

$\begin{gathered} 10-0=9.8\times t \\ t=\frac{10}{9.8} \\ t=1.02\text{ s} \end{gathered}$

Thus, the time for which the acorn in the air is 1.02 second.