Question

You drop your cell phone while in the bathroom in front of the mirror while the water is runring inthe sink below. If you are 0.45 meters above the sink, how long do you have before your cell phone isruined?

Answer 1

0.303 seconds

Step-by-step explanation:

We need to find the time that the cell phone takes to reach the sink. So, we will use the following equation

`y=y_i+v_it+(1)/(2)at^2`

Where

yi is the initial position, so yi = 0.45 m

vi is the initial velocity. Since it is freefall, vi = 0 m/s

a is the acceleration due to gravity, so a = -9.8 m/s²

y is the final position, so y = 0 m

t is the variable that we need to find.

So, replacing the values, we get:

`\begin{gathered} 0=0.45+0t+(1)/(2)(-9.8)t^2 \\ 0=0.45-4.9t^2 \end{gathered}`

Now, we can solve for t

`\begin{gathered} -0.45=-4.9t^2 \\ (-0.45)/(-4.9)=t^2 \\ 0.09=t^2 \\ \sqrt[]{0.09}=t \\ 0.303\text{ s = t} \end{gathered}`

Therefore, you have 0.303 seconds before your cell phone is ruined.