A Coyote and a Rat#
A coyote notices a rat running past it, toward a bush where the rat will be safe. The rat is running with a constant velocity of \(v\_{\text{rat}} = {{ params.v_r }} \rm{m/s}\) and the coyote is at rest, \(\Delta x = {{ params.d_x }} \rm{m}\) to the left of the rat. However, at \(t=0 \rm{s}\), the coyote begins running to the right, in pursuit of the rat, with an acceleration of \(a\_{\text{coyote}} = {{ params.a_c }} \rm{m/s^2}\).
Set your reference frame to be located with the origin at the original location of the coyote and the rightward direction corresponding to the positive \(x\)-direction.
Part 1#
Write the position of the coyote as a function of time \(x\_{\text{coyote}}(t)\). Do not plug in numerical values for this part.
Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.
For |
Use |
|---|---|
\(t\) |
t |
\(\Delta x\) |
dx |
\(v\_{\text{rat}}\) |
vr |
\(a\_{\text{coyote}}\) |
ac |
Answer Section#
Part 2#
Write the velocity of the coyote as a function of time \(v\_{\text{coyote}}(t)\). Do not plug in numerical values for this part.
Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.
For |
Use |
|---|---|
\(t\) |
t |
\(\Delta x\) |
dx |
\(v\_{\text{rat}}\) |
vr |
\(a\_{\text{coyote}}\) |
ac |
Answer Section#
Part 3#
Write the position of the rat as a function of time \(x\_{\text{rat}}(t)\). Do not plug in numerical values for this part.
Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.
For |
Use |
|---|---|
\(t\) |
t |
\(\Delta x\) |
dx |
\(v\_{\text{rat}}\) |
vr |
\(a\_{\text{coyote}}\) |
ac |
Answer Section#
Part 4#
Write the velocity of the rat as a function of time \(v\_{\text{rat}}(t)\). Do not plug in numerical values for this part.
Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.
For |
Use |
|---|---|
\(t\) |
t |
\(\Delta x\) |
dx |
\(v\_{\text{rat}}\) |
vr |
\(a\_{\text{coyote}}\) |
ac |
Answer Section#
Part 5#
At what time does the coyote catch the rat \(t\_{\text{catch}}\)?
Answer Section#
Please enter in a numeric value in \(\rm{s}\).
Part 6#
At this time, what is the velocity of the coyote \(v\_{\text{coyote}}(t\_{\text{catch}})\)?
Answer Section#
Please enter in a numeric value in \(\rm{m/s}\).
Part 7#
At this time, what is the velocity of the rat \(v\_{\text{rat}}(t\_{\text{catch}})\)?
Answer Section#
Please enter in a numeric value in \(\rm{m/s}\).
Part 8#
What is the location at which the coyote will catch the rat \(x\_{\text{coyote}}(t\_{\text{catch}}) = x\_{\text{rat}}(t\_{\text{catch}})\)?
Answer Section#
Please enter in a numeric value in \(\rm{m}\).
Attribution#
Problem is licensed under the CC-BY-NC-SA 4.0 license.
