Question

What is the best estimate for the time required for an object in free fall (Vi = 0) with air resistance to travel 313.6 m.

Answer 1

Answer:

Third option

Explanation:

We will find the answer by using the formulas to calculate distance during a free fall...

$s=(\frac{1}{2})gt^2$

t = fall time

g = free all acceleration

We know that the initial velocity is 0, and the acceleration the object has before it hits the ground is 313.6 m, we also know that acceleration while free falling is a constant 9.80665 meters per second (default meters per second) and that is with air resistance (which is also constant) so we are going to use 8 seconds because it is mentioned twice in the options provided. Knowing all of this data we can correctly substitute to find the amount of time using the formulas of free fall.

s = (1/2)gt^2 = 0.5 × 9.80665 × 8^2 = 313.8m

But since we want the object to travel 313.6m the time it needs has to be a little less then 8 seconds which is the third option.

Hope this helps.

Answer 2

Answer:

$s = v_it + \frac{1}{2} g {t}^{2} \\ t = \sqrt{2 \frac{s}{g} } \\ t = \sqrt{2 \times \frac{313.6}{9.81} } \: sec \\ = 7.995 \: sec \approx \: a \: little \: less \\ than \: 8 \: sec$