Hello again,
Well, here is the logic behind my concerns...
The cop starts out at 200 feet north of the intersection.
He has good eyesight (he he) and so he is prompted to start
heading south at 400 ft per sec to catch up with the 'speeder'
he sees, who is traveling at 200 ft per sec east.
The equation for distance between cop and speeder for this problem is:
s(t)=sqrt((400*t-200)^2+(200*t)^2)
because the cop is going at 400*t and the speeder at 200*t
and the cop starts out at -200 feet from the intersection and
they are traveling at right angles to each other.
Now the derivative is:
ds/dt=(1000*t-400)/sqrt(5*t^2-4*t+1)
and solving this for zero (0) we get:
0=(1000*t-400)/sqrt(5*t^2-4*t+1)
and so when ds/dt=0, t equals 0.4 seconds.
What this means is that for any time less than 0.4 seconds the
derivative is negative, and for any time more than 0.4 seconds the
derivative is positive.
Thus, for t=2 seconds, the derivative (rate of change of distance
between cop and speeder) is positive.
This means the problem is not stated correctly or something else
is wrong. For example, perhaps the time t to solve for is 0.2 seconds
rather than 2.0 seconds, which would make the derivative negative
and around -316 ft/sec like the so called 'correct' stated answer to
this problem.
It's easy to make a mistake like this because it only involves leaving
out the decimal point from the .2 to make it incorrectly 2 instead.
This means the original 'correct' statement for the problem probably read like this:
Originally Posted by
magician13134 but corrected here...
A policeman is parked 200 ft north of an intersection. He sees a reckless driver who is traveling due east through the intersection. The driver is traveling at 200ft/s. If the police leaves the intersection immediately traveling due south at 400ft/s, find the rate of change of the distance between the police and driver after 0.2 seconds.
Thanks
Note that i changed "2 seconds" to "0.2 seconds".
Answer: -316.2267778 feet per second.
Here is a graph of the distance and the rate of change of distance from t=0 to t=2 seconds...
**broken link removed**