KindofSlow
Junior Member
- Joined
- Mar 5, 2010
- Messages
- 90
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
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
