IMO, dz/dt should be positive since it is being pulled in the positive x and y directions (up and rightwards). This would give a positive answer (+2.077 m/s), which answers the original problem more accurately.
"How fast is the boat approaching the dock?" -- it is in fact approaching at positive 2.077 m/s, not negative.
I disagree about dz/dt being positive since z is the length of the hypotenuse of the right triangle used to solve this problem and that distance is not increasing...
I agree, "fast" sort of implies "speed" ...but the answer was listed as negative in the student's answer key who submitted this question, so...
It should be negative. The person who wrote that is not realizing that the cartesian plane is flipped. Your triangle is backwards according to convention. Rightwards in your example is not positive. The -2.077 m/s tells you that x is decreasing at a rate of 2.077 m/s. So if someone asked for a speed, its 2.077 m/s, but if they ask for a velocity, which tells you more accurately what's going on, its -2.077 m/s. How fast, in math terms, is pretty ambiguous as to which one its really asking for.
@pickedupapencil I see your point. The problem does mention that the boat is approaching the dock...approach is a funny word in math though as well...
thaaaank youuu so much!!!!!!!!
FunTimesWithGabbi 2 weeks ago
IMO, dz/dt should be positive since it is being pulled in the positive x and y directions (up and rightwards). This would give a positive answer (+2.077 m/s), which answers the original problem more accurately.
"How fast is the boat approaching the dock?" -- it is in fact approaching at positive 2.077 m/s, not negative.
apiersall 2 years ago
I disagree about dz/dt being positive since z is the length of the hypotenuse of the right triangle used to solve this problem and that distance is not increasing...
I agree, "fast" sort of implies "speed" ...but the answer was listed as negative in the student's answer key who submitted this question, so...
neiljodymath 2 years ago
It should be negative. The person who wrote that is not realizing that the cartesian plane is flipped. Your triangle is backwards according to convention. Rightwards in your example is not positive. The -2.077 m/s tells you that x is decreasing at a rate of 2.077 m/s. So if someone asked for a speed, its 2.077 m/s, but if they ask for a velocity, which tells you more accurately what's going on, its -2.077 m/s. How fast, in math terms, is pretty ambiguous as to which one its really asking for.
pickedupapencil 1 year ago
@pickedupapencil I see your point. The problem does mention that the boat is approaching the dock...approach is a funny word in math though as well...
neiljodymath 1 year ago
oh my bad , sorry
mozam007 2 years ago
not a problem, I dont want to have have wrong stuff up there...thanks for the comments
neiljodymath 2 years ago
z= 25;
x= 24
x does not equal 25 . read the problem carefully.
mozam007 2 years ago
how's that?
read the problem carefully...
"the bow of the boat is 25 meters from a point that is directly below the pulley"
the bow is where the rope is attached and the bow is 25 m horizontal distance from a point directly below the pulley.
How do you interpret this?
neiljodymath 2 years ago