KindofSlow
Junior Member
- Joined
- Mar 5, 2010
- Messages
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From this site:
Exercise 6.2.13:
The trough shown in figure 6.2.6 is constructed by fastening together three slabs of wood of dimensions 10 ft × 1 ft, and then attaching the construction to a wooden wall at each end. The angle θ was originally 30∘, but because of poor construction the sides are collapsing. The trough is full of water. At what rate (in ft33/sec) is the water spilling out over the top of the trough if the sides have each fallen to an angle of 45∘, and are collapsing at the rate of 1∘ per second?
My work:
v = 10*sinθ*cosθ +10
dv/dt=(10*sinθ*(-sinθ)+10*cosθ*cosθ)*dθ/dt
dv/dt=10*cos(2θ)*dθ/dt
cos(90 degrees) = 0 which is obviously wrong.
I cannot find where my mistake is.
Any assistance telling me where my mistake is will be greatly appreciated.
Thank you
6.2 Related Rates
www.whitman.edu
The trough shown in figure 6.2.6 is constructed by fastening together three slabs of wood of dimensions 10 ft × 1 ft, and then attaching the construction to a wooden wall at each end. The angle θ was originally 30∘, but because of poor construction the sides are collapsing. The trough is full of water. At what rate (in ft33/sec) is the water spilling out over the top of the trough if the sides have each fallen to an angle of 45∘, and are collapsing at the rate of 1∘ per second?
My work:
v = 10*sinθ*cosθ +10
dv/dt=(10*sinθ*(-sinθ)+10*cosθ*cosθ)*dθ/dt
dv/dt=10*cos(2θ)*dθ/dt
cos(90 degrees) = 0 which is obviously wrong.
I cannot find where my mistake is.
Any assistance telling me where my mistake is will be greatly appreciated.
Thank you
