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
(1/2)*a*t^2 = 0.300
To calculate the reaction time of the student and estimate the minimum average speed of nerve impulses, we need to understand the physics behind the scenario.
(a) Calculating the reaction time:
The reaction time is the time it took for the student to respond and catch the meterstick after it was dropped. We can use the equation:
Reaction time = Distance / Velocity
Since the meterstick fell a distance of 0.300 meters before being caught, we only need to calculate the velocity.
To measure the velocity of the meterstick, we need to use the equations of motion. In this case, we can use the equation for free fall:
s = ut + (1/2)at^2
where:
s = displacement (0.300 meters)
u = initial velocity (0 m/s, as the meterstick was initially at rest)
a = acceleration due to gravity (-9.8 m/s^2, assuming no air resistance)
t = time
Rearranging the equation, we get:
t = sqrt((2s) / a)
t = sqrt((2 * 0.300 m) / -9.8 m/s^2)
t ≈ 0.240 seconds
Therefore, the student's reaction time is approximately 0.240 seconds.
(b) Estimating the minimum average speed of nerve impulses:
To estimate the minimum average speed of nerve impulses, we can use the reaction time and the distance the nerve impulses need to travel. In this case, we assume the distance traveled is the length of the student's arm from her eye to her hand, which we'll estimate as 0.70 meters.
Speed = Distance / Time
Using the reaction time calculated earlier (0.240 seconds) and the distance (0.70 meters), we can find the minimum average speed:
Speed = 0.70 m / 0.240 s
Speed ≈ 2.92 m/s
Therefore, the estimated minimum average speed of the nerve impulses traveling from the student's eye to her brain and back to her hand is approximately 2.92 meters per second.