Question

Improperly installed air conditioners can occasionally fall from apartment windows down onto the road below.  How long does a pedestrian have to get out of the way of an air conditioner falling eight stories [24m] hello I just need help idea my vi vf t d a and I am not certain if it is a horizontal question or not

Answer 1

Given data:

* The distance traveled by the air conditioner is,

$d=24\text{ m}$

Solution:

As the air conditioner is falling freely under the action of gravity.

Thus, the acceleration of the air conditioner is equal to the acceleration due to gravity.

$\begin{gathered} a=g \\ a=9.8ms^{-2} \end{gathered}$

As the air conditione ris falling itself from the height.

Thus, the initial velocity of the air conditoner is,

$v_i=0\text{ m/s}$

By the kinematics equation, the final velocity of the air conditioner is,

$v^2_f-v^2_i=2ad$

Substituting the known values,

$\begin{gathered} v^2_f-0=2\times9.8\times24 \\ v^2_f=470.4 \\ v_f=21.69\text{ m/s} \end{gathered}$

Thus, the final velocity of the air conditioner is 21.69 m/s.

By the kinematics equation, the time taken by the air conditioner,

$v_f-v_i=at$

where t is the time taken by the air conditioner to reach the ground,

Substituting the known values,

$\begin{gathered} 21.69-0=9.8t \\ t=\frac{21,69}{9.8} \\ t=2.21\text{ s} \end{gathered}$

Thus, the time taken by the air conditioner ot reach the ground is 2.21 seconds.