I'm having some trouble with a few problems involving derivatives and rates. Here's one of the ones that is confusing me:(adsbygoogle = window.adsbygoogle || []).push({});

A waterskier skis over the ramp shown in the figure at a speed of 30ft/s. How fast is she rising as she leaves the ramp?

The ramp is a right triangle facing the waterskier so that they can go up it, with sides of (assume y is the vertical axis, x is horizontal, z is hypotenuse) x = 15ft, y = 4ft, and by the pythagorean theorem, z = [tex]\sqrt{241}[/tex]

The first problem I was having here, is whether or not the speed given is relative to the x axis, or the z axis? I would think generally the x axis, but the problem states "over the ramp". Also, when doing the problem for the speed given on the x axis I got a negative number for dy/dt. When doing it given on the z axis I get about 116ft/s, which seems too fast.

Assuming it's on the x I set it up like so (I wasn't sure if I should use z^2, but I don't know what dz/dt is so I didn't...):

[tex]x^2 + y^2 = \sqrt{241}[/tex]

[tex]2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0[/tex]

[tex]900 + 8 \frac{dy}{dt} = 0[/tex]

[tex]\frac{dy}{dt} = \frac{-225}{2}[/tex]

Which doesn't make any sense. Where am I going wrong here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Derivatives and rates

**Physics Forums | Science Articles, Homework Help, Discussion**