The Student Room Group

c4 differentiation QSN, some1 help plizz

At time t=0, a tank of height 2metres is completely filled with water. water then leaks from a whole in the side of the tank such that the depth of water in the tank, 'y' metres, after 't' hours satisfies the differential equation :

dy/dt = -k
Unparseable latex formula:

e^

^(-0.2t)

where k is a positive constant

a) find an expression for 'y' in terms of k and t
given that 2 hours after being filled the depth of water in the tank is 1.6 metres,
b) find the velue for k to 4 sig.figures

c) given also that the whole in the tank is 'h' centimetres above the base of the tank, show that 'h' = 79 to 2 sig.figures




for part a, i intergrated that dy/dt , then substituted the y and t values to work out k(for part b)
i think i did somethin wrong in the process thoh

in part C, im trying dy/dx =0, im not sure bout this thoh

could some1 show me how to do this qsn pliz
Reply 1
TEE001
At time t=0, a tank of height 2metres is completely filled with water. water then leaks from a whole in the side of the tank such that the depth of water in the tank, 'y' metres, after 't' hours satisfies the differential equation :

dy/dt = -k
Unparseable latex formula:

e^

^(-0.2t)

where k is a positive constant

a) find an expression for 'y' in terms of k and t
given that 2 hours after being filled the depth of water in the tank is 1.6 metres,
b) find the velue for k to 4 sig.figures

c) given also that the whole in the tank is 'h' centimetres above the base of the tank, show that 'h' = 79 to 2 sig.figures




for part a, i intergrated that dy/dt , then substituted the y and t values to work out k(for part b)
i think i did somethin wrong in the process thoh

in part C, im trying dy/dx =0, im not sure bout this thoh

could some1 show me how to do this qsn pliz



dy/dt=-ke^(-0.2t)
so y=5ke^(-0.2t)+C

when t=0, y=2, so C+5k=2, so C=2-5k

so y=5ke^(-0.2t)+2-5k, then
1.6=5ke^(-0.4)+2-5k
so k=0.2427

I think.....at least I'm pretty sure that's the right method :smile:
Reply 2
thanks, i wasnt adding the 'C' for some reason:mad:
Reply 3
TEE001
thanks, i wasnt adding the 'C' for some reason:mad:



I always forget the 'C's also
Reply 4
so how do you figure out part c)...still confused??????