as we saw earlier, the distance z is
z^2 = 1+x^2
z dz/dt = x dx/dt
plugging in the numbers,
z(3) = ?10, so
?10 dz/dt = 3 * 2
dz/dt = 6/?10 = 1.897
So, I guess you were right on that one.
As for dz/dt when x gets large, consider that
z^2 = 1+x^2
as x gets large, that is just
z^2 ? x^2
z dz/dt ? x dx/dt
But z ? x, so, when the boat is far away, the rope's speed approaches the boat's speed.
http://www.wolframalpha.com/input/?i=derivative+sqrt(1%2Bx%5E2)
A boat pulls away from a dock at 2 m/s, but the operator has neglected to remove the tow rope used to pull the boat up to the dock. This rope runs thru a pulley which is attached to the dock at a point 1 m higher than the point at which the rope is attached to the boat.
A) How fast is the rope being pulled out when the boat is 3 m away from the dock?
Potential Answer: got 1.89m/s, but not entirely sure if I'm doing this correctly.
B) How fast is the rope is pulled as the distance from the dock grows large? Justify your answer
Potential Answer: If the rope gets larger, the speed of the rope increases as well?
1 answer
2 answers