Question

Scientists have investigated how quickly hoverflies start beating their wings when dropped both in complete darkness and in a lighted environment. Starting from rest, the insects were dropped from the top of a 40-cm-tall box. In the light, those flies that began flying 200 ms after being dropped avoided hitting the bottom of the box 80% of the time, while those in the dark avoided hitting only 22% of the time.
A. How far would a fly have fallen in the 200 ms before it began to beat its wings?

B. How long would it take for a fly to hit the bottom if it never began to fly? In seconds.

Answer 1

Answers:

A) 0.204 m

B) 0.285 s

Explanation:

Answer A:

This described situation is free fall, this means the initial velocity of the fly is zero, and the equation that will be used is:

$y=y_{o}+V_{o}t-\frac{1}{2}gt^{2}$ (1)

Where:

$y$ is the final height of the fly

$y_{o}=40 cm=0.4 m$ is the initial height of the fly

$V_{o}=0$ is the initial velocity of the fly

$t=200(10)^{-3} s$ is the time

$g=9.8 m/s^{2}$ is the acceleration due to gravity

$y=0.4 m+0-\frac{1}{2}(9.8 m/s^{2})(200(10)^{-3} s)^{2}$ (2)

$y=0.204 m$ (3)  This is the distance at which the fly would begin to beat its wings

Answer B:

In this part we will also use equation (1), but we will find the time:

$y=y_{o}+V_{o}t-\frac{1}{2}gt^{2}$ (1)

Where:

$y=0$ is the final height of the fly

$y_{o}=40 cm=0.4 m$ is the initial height of the fly

$V_{o}=0$ is the initial velocity of the fly

$t$ is the time  we need to find

$g=9.8 m/s^{2}$ is the acceleration due to gravity

$0=0.4 m+0-\frac{1}{2}(9.8 m/s^{2})t^{2}$ (4)

Isolating $t$:

$t^{2}=\frac{(-2)(-0.4 m)}{9.8 m/s^{2}}$ (5)

$t=0.285 s$ (6)  This is the time it would take for a fly to hit the bottom of the box