A biophysics student measures her reaction time by having a friend drop a meterstick between her
fingers. The meterstick falls 0.300 meters before she catches it.
(a) What is her reaction time?
(b) Estimate the minimum average speed of nerve impulses going from her eye to her brain and then
back to her hand.
.3=4.9t^2
solve for time t.
avg speed=distance/time=1m/time
To find the answers to these questions, we need to use the information provided and some basic physics principles.
(a) To calculate the reaction time, we need to use the equation of motion. Let's assume that the meterstick is dropped from rest, and neglect the air resistance. The equation we can use is:
d = (1/2)at^2
where:
d is the distance traveled by the falling meterstick (0.300 meters)
a is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken to catch the meterstick (reaction time)
To find the reaction time, we rearrange the equation:
t = sqrt(2d/a)
Substituting the given values:
t = sqrt(2 * 0.300 m / 9.8 m/s^2)
By plugging this equation into a calculator, we find that the reaction time is approximately 0.242 seconds.
(b) To estimate the minimum average speed of nerve impulses, we need to consider the distance traveled by the nerve impulse. The distance consists of the length of the nerve pathway from the eye to the brain and back to the hand. As an estimation, we can assume this distance to be the length of a human arm, which is around 0.8 meters.
Since the nerve impulse travels from the eye to the brain and then back to the hand, we need to consider the total distance traveled, which is twice the distance of the human arm.
To find the average speed, we divide the total distance by the total time taken:
Average speed = Total distance / Total time
The total distance is 2 * 0.8 m = 1.6 meters, and the total time is the sum of the reaction time and the time taken for the impulse to travel back:
Total time = reaction time + time taken for nerve impulse
Given the reaction time as 0.242 seconds, we need to estimate the time taken for the nerve impulse. According to the estimated speed data, the speed of nerve impulses can vary between 0.61 m/s to 119 m/s. Therefore, we can assume a conservative estimate of 1 m/s.
Total time = 0.242 s + (1.6 m / 1 m/s)
By calculating this equation, the total time is approximately 1.842 seconds.
Now, we can calculate the average speed:
Average speed = 1.6 m / 1.842 s
After performing the calculation, the estimated minimum average speed of nerve impulses going from her eye to her brain and back to her hand is approximately 0.869 m/s.
Note: These calculations are based on estimations and assumptions, so the actual values may differ to some extent.