Catching a Ruler

Q. A friend lets go of a ruler held between your fingers, and you catch it after it has fallen 21.0 cm. Taking g as 9.8 m/s², what is your reaction time, in seconds? expects 0.21 s

What the draft establishes

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The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A friend lets go of $v_{0} = 0$ m/s a ruler held between your fingers, and you catch it after it has fallen $a = - g$ 21.0 cm $x_{1} = -21.0$ cm. Taking g as 9.8 m/s² $g = 9.8$ m/s², what is your reaction time, in seconds?

The playground

Inputs

gravity

g

9.8 m/s²

Outputs

reaction time

Δ t

The solution

Solved with UniformAcceleration

Given

$g = 9.8$ m/s²
$v_{0} = 0$ m/s from “lets go of”
$x_{1} = -21.0$ cm from “fallen” and “21.0 cm”
$a = - g$ from “fallen”

Assumed

$x_{0} = 0$ m

Find $Δ t$ .

Working

$x_{1} = -21.0$ cm $= −0.21$ m
fallen $a = - g$
$a = - 9.8$
$a = −9.8$ m/s²
position after a time(falling) $x_{1} = x_{0} + v_{0} \cdot Δ t + \frac{a \cdot {Δ t}^{2}}{2}$
$(−0.21) = 0 + 0 \cdot Δ t + \frac{(−9.8) \cdot {Δ t}^{2}}{2}$
$Δ t = 0.21 s$
$Δ t \approx 0.21$ sto 2 significant figures

Conclusion

The ruler falls freely from rest the whole time you take to react, so the distance it falls is a clock.

The Ruby

1require_relative "../physics"23question :catching_a_ruler do4  kind :numerical5  describes "A friend lets go of a ruler held between your fingers, and you catch it after it has " \6          "fallen 21.0 cm. Taking g as %{gravity}, %{reaction_time}, in seconds?"7  given gravity: "9.8 m/s2"8  asks reaction_time: "what is your reaction time"9end

1require_relative "../questions/catching_a_ruler"2require_relative "../science/motion_in_a_straight_line/uniform_acceleration"34solve :catching_a_ruler, using: UniformAcceleration do5  objects :ruler6  ruler.goes(:falling)78  take gravity: g9  assume ruler.initial_position => "0 m"10  deduce_from "lets go of", ruler.initial_velocity => "0 m/s"11  deduce_from "fallen", ruler.acceleration => -g12  deduce_from "fallen", "21.0 cm", ruler.final_position => "-21.0 cm"13  take reaction_time: falling.time_taken14  answer find_value(:reaction_time, in: "s", figures: 2)1516  conclusion "The ruler falls freely from rest the whole time you take to react, so the distance " \17             "it falls is a clock."18end

1require_relative "../solutions/catching_a_ruler"23play_with :catching_a_ruler do4  title "Catching a Ruler"5end

The laws

quantity	written	units	within	from
position	$x$	m	—	Velocity
displacement	$Δ x$	m	—	Velocity
path length	$d$	m	—	Velocity
time taken	$Δ t$	s	0 … 1e+05	Velocity
average velocity	$v_{av}$	m/s	—	Velocity
average speed	$c_{av}$	m/s	—	Velocity
starting position	$x_{0}$	m	—	Velocity
final position	$x$	m	—	Velocity
velocity	$v$	m/s	—	Acceleration
change of velocity	$Δ v$	m/s	—	Acceleration
average acceleration	$a_{av}$	m/s²	—	Acceleration
starting velocity	$v_{0}$	m/s	—	Acceleration
final velocity	$v$	m/s	—	Acceleration
acceleration	$a$	m/s²	—	UniformAcceleration
gravity	$g$	m/s²	—	UniformAcceleration
time	$t$	s	0 … 1e+05	UniformAcceleration
displacement of ruler during falling	$Δ x$	m	—
position of ruler at end of falling	$x_{1}$	m	—
position of ruler at start of falling	$x_{0}$	m	—
average velocity of ruler during falling	$v_{av}$	m/s	—
time taken of falling	$Δ t$	s	0 … 1e+05
average speed of ruler during falling	$c_{av}$	m/s	—
path length of ruler during falling	$d$	m	—
change of velocity of ruler during falling	$Δ v$	m/s	—
velocity of ruler at end of falling from ground	$v_{1}$	m/s	—
velocity of ruler at start of falling from ground	$v_{0}$	m/s	—
average acceleration of ruler during falling	$a_{av}$	m/s²	—
acceleration of ruler during falling	$a$	m/s²	—

x_{0} \equiv x_{i} (start of motion)

starting position

x \equiv x_{i} (end of motion)

final position

v_{0} \equiv v_{i} (start of motion)

starting velocity

v \equiv v_{i} (end of motion)

final velocity

t \equiv Δ t_{m}

time

d_{i} (whole) = d_{i} (part 1) + d_{i} (part 2)

path in parts

Δ t_{w} = Δ t_{p} + Δ t_{p}

time in parts

a_{i} (part 1) = a_{i} (whole)

steady through its parts

Δ x = x_{1} - x_{0}

change of position(falling)

v_{av} = \frac{Δ x}{Δ t}

displacement a time(falling)

c_{av} = \frac{d}{Δ t}

path a time(falling)

Δ v = v_{1} - v_{0}

velocity gained(falling)

a_{av} = \frac{Δ v}{Δ t}

velocity gained a time(falling)

v_{1} = v_{0} + a \cdot Δ t

velocity after a time(falling)

x_{1} = x_{0} + v_{0} \cdot Δ t + \frac{a \cdot {Δ t}^{2}}{2}

position after a time(falling)

{v_{1}}^{2} = {v_{0}}^{2} + 2 \cdot a \cdot (x_{1} - x_{0})

velocity after a distance(falling)

x_{1} - x_{0} = \frac{(v_{1} + v_{0}) \cdot Δ t}{2}

mean of the velocities(falling)

a = - g

fallen