A triangular trench 40ft long is 2ft across the top, and 2ft deep. If water flows in at the rate of 3ft³/min, find how fast the surface is rising when the water is 6 in deep.
2 answers
Jawab la soalan tu sendiri.Tanya2 pulak
Draw a diagram. It should be clear that when the water has depth y ft, the cross-section of water has area y^2/2 ft^2. So, the volume
v = 20y^2
dv/dt = 40y dy/dt
when y = 6 in = 1/2 ft,
3 = 40(1/2) dy/dt
now just solve for fy/dt, the rate the depth is changing. That is, how fast the surface is rising.
v = 20y^2
dv/dt = 40y dy/dt
when y = 6 in = 1/2 ft,
3 = 40(1/2) dy/dt
now just solve for fy/dt, the rate the depth is changing. That is, how fast the surface is rising.
2 answers