Reaction time tests

[Roylan]

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
40cm.

(c) Make d the subject of the equation, remembering to use your simplified version of
d/? 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 40 cm.

 

[Deleted member 4993]

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
40cm.

(c) Make d the subject of the equation, remembering to use your simplified version of
d/? 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 40 cm.

I think the given equation should look like:

$\displaystyle \text t \ = \ \sqrt{\frac{2d}{9.8}}$

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment.

for part (a), rewrite the given equation as:

$\displaystyle \text t \ = \ \sqrt{\frac{d}{\left (\frac{9.8}{2}\right )}}$

and continue......

 

[Steven G]

Roylan, this is a math help forum. That is the helpers help students like you solve problems which they are having difficulty with. It is not a drop off your homework and come back later for the solution type of site.

We want you to be actively involved in solving your problems. In fact we prefer that you are the one who solves your problems with the help of the helpers giving you hints, etc so that you can solve the problem yourself.

 

[scottbrandon]

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
40cm Human Benchmark Online.

(c) Make d the subject of the equation, remembering to use your simplified version of
d/? 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 40 cm.

(a) t=d4.902t = \sqrt{\frac{d}{4.902}}t=4.902d

(b) Reaction time is approximately 0.286 seconds0.286 \, \text{seconds}0.286seconds.

(c) d=9.8t22d = \frac{9.8t^2}{2}d=29.8t2

(d) The ruler should fall approximately 0.1 m0.1 \, \text{m}0.1m (or 10 cm10 \, \text{cm}10cm).

 

[Dr.Peterson]

(a) $t = \sqrt{\frac{d}{4.902}}$

(b) Reaction time is approximately $0.286 \, \text{seconds}$.

(c) $d = \frac{9.8t^2}{2}$

(d) The ruler should fall approximately $0.1 \, \text{m}$ (or $10 \, \text{cm}$).

You seem to have pasted from some other place, which messed up the LaTeX. I've edited what you wrote above, so you should check that it is what you meant.

This looks sort of correct, except that

• You apparently changed 9.8 as in the problem to 9.804 from some other source (which is not this source). With your rounding, that doesn't make a difference in the numerical answers.
• You failed to use the simplification from part (a) as directed.
• And 0.1 m is not 10 cm!

 

[khansaheb]

Roylan, this is a math help forum. That is the helpers help students like you solve problems which they are having difficulty with. It is not a drop off your homework and come back later for the solution type of site.

We want you to be actively involved in solving your problems. In fact we prefer that you are the one who solves your problems with the help of the helpers giving you hints, etc so that you can solve the problem yourself.

This problem was first posted ~

• Mar 17, 2020 - and the original poster disappeared......