I'm stuck on this related rate problem.
A water skier skis over a ramp that is 15 ft long and 4 ft high, at a speed of 30 ft/s. How fast is she rising as she leaves the ramp?
This is what I calculated please tell me if its right or wrong.
Given: x^2+y^2=z^2, dz/dt=30ft/s, x=15, y=4
Unknown: z, dx/dt, dy/dt
x^2 + y^2 = z^2
15^2 + 4^2 = z^2
z = √241
To get the 30 ft/s, multiply sides of the triangle by 30/√241.
So, 15*30/√241 and 4*30/√241 => dx/dt = 450/√241 and dy/dt = 120/√241
So Chain rule: x^2 + y^2 = z^2 => 2x*dx/dt + 2y*dy/dt = 2z*dz/dt
2(15)*450/√241 + 2(4)120/√241 = 2(√241)30
13500/√241 + 960/√241 = 60/√241
=>60/√241 = 60/√241
So she's rising at a rate of 60√241 ft/s.