A squirrel drops an acorn from a tree. If the observer is 4 m below, how much time do they have to avoid it?

To determine how much time the observer has to avoid the acorn, we can use the kinematic equation that relates the distance an object falls under the influence of gravity to time. The equation is:

[

d = \frac{1}{2} g t^2

]

where ( d ) is the distance (4 meters in this case), ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )), and ( t ) is the time in seconds. Rearranging the equation to solve for time gives us:

[

t = \sqrt{\frac{2d}{g}}

]

Substituting in the values:

[

t = \sqrt{\frac{2 \times 4 , \text{m}}{9.8 , \text{m/s}^2}}

]

Calculating the numerator:

[

2 \times 4 = 8 , \text{m}

]

Now divide by ( g ):

[

\frac{8}{9.8} \approx 0.816 , \text{s}

]

Taking the square root