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.
(a) To calculate the reaction time, we can use the kinematic equation:
d = 0.5 * a * t^2
where:
d = distance (0.300 m)
a = acceleration (assuming constant and due to gravity, a = 9.8 m/s^2)
t = time (reaction time)
Rearranging the equation to solve for time:
t = sqrt((2 * d) / a)
t = sqrt((2 * 0.300 m) / 9.8 m/s^2)
t ≈ sqrt(0.061 m /s^2)
t ≈ 0.25 s
Therefore, her reaction time is approximately 0.25 seconds.
(b) The minimum average speed of nerve impulses can be estimated by assuming that the nerve impulse travels from the eye to the brain and then back to the hand. This is a round trip, so we can calculate the average speed using the formula:
Average speed = Total distance / Total time
The total distance is twice the initial distance (0.300 m) since it's a round trip:
Total distance = 2 * 0.300 m = 0.600 m
The total time is twice the reaction time (0.25 s) since it includes the round trip:
Total time = 2 * 0.25 s = 0.50 s
Average speed = 0.600 m / 0.50 m = 1.20 m/s
Therefore, the estimated minimum average speed of nerve impulses is approximately 1.20 m/s.
To calculate the reaction time of the biophysics student, we need to use the formula for distance traveled:
distance = (1/2) * acceleration * time^2
In this case, the distance traveled is given as 0.300 meters. However, since the student catches the meterstick, the initial velocity is 0. Therefore, the formula simplifies to:
distance = (1/2) * acceleration * time^2
Plugging in the values:
0.300 = (1/2) * acceleration * time^2
We can rearrange this equation to solve for time:
time^2 = (2 * distance) / acceleration
(a) To calculate the reaction time, we need to know the value of acceleration. Since the person is dropping the meterstick, it is subjected to the acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Plugging in the values:
time^2 = (2 * 0.300) / 9.8
time^2 = 0.6122
Taking the square root of both sides:
time = √0.6122
time ≈ 0.782 seconds
Therefore, the reaction time of the biophysics student is approximately 0.782 seconds.
(b) To estimate the minimum average speed of nerve impulses, we need to consider the time it takes for the student to see the meterstick falling (from her eye to her brain) and then react by catching it (from her brain to her hand).
First, let's assume that half of the reaction time is spent on visual processing and half on transferring the signal from the brain to the hand.
Visual processing time = 0.782 / 2 = 0.391 seconds
Since the distance traveled by the nerve impulses is equal to the distance the meterstick falls (0.300 meters), we can calculate the average speed using:
average speed = distance / time
average speed = 0.300 meters / 0.391 seconds
average speed ≈ 0.767 m/s
Therefore, the minimum average speed of nerve impulses going from the student's eye to her brain and then back to her hand is approximately 0.767 m/s.
a. h = 0.5*g*t^2 = 0.4 m.
g = 9.8 m/s^2.
t = ?