Question

Reaction time tests can be used to assess an individual’s hand-eye coordination. One
test involves catching a 1 metre ruler and measuring the distance, d in metres, that the ruler travelled before being caught. The reaction time t seconds is then calculated using the formula:

= √2d/9.8

(a) Simplify the expression 2d/9.8 under the square root sign to d/?

(b) Calculate the reaction time if the distance the ruler fell before being caught was
44cm.

(c) Make d the subject of the equation, remembering to use your simplified version of
2d/9.8 which you found in part (a).

(d) Use your equation from part (c) to find the distance the ruler should fall before being caught if t is half the value you found in part (b), i.e. half the time taken to catch the ruler when it fell 44 cm.

Answer 1

Given : Reaction time tests

The reaction time t seconds is then calculated using the formula:

= √2d/9.8

To Find :  Calculate the reaction time if the distance the ruler fell before being caught was 44cm.

find the distance the ruler should fall before being caught if t is half the value for 44 cm

Solution:

t  = √2d/9.8

=>t = √d/4.9

=> t  = √10d/49

=> t =  (1/7) √10d

squaring both sides

t²  = 10d/49

d = 49t²/10

=> d = 4.9t²

t =  (1/7) √10d

d = 44 cm  = 0.44 m

=> t   = (1/7) √(10 * 0.44)

=> t = 0.3 secs

d = 4.9t²

t = 0.3

d = 4.9(0.3)²  = 0.44 m  = 44 cm

t = 0.3/2  = 0.15

d = 4.9(0.3/2)² = 0.44/4 m = 0.11 m = 11 cm

the distance the ruler should fall before being caught = 11 cm   if t is half the value compared to distance 44 cm.

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