yr 12: physical applications (1 Viewer)

[-pari-]

(1) a conical vessel is arranged with the vertex downwards and initially contains water to a height of 10. a small tap is opened at the vertwx and the water leaks away in such a way that after t min, the rate of decrease of the height h cm of water in the vessel is given by 5t/4cm/min. calculate the time taken for the vessel to empty and the height of the water after 2 min.
anwers: 4min; 7.5 cm

didn't know what to make of the 5t/4cm/min.....??

(2) the rate of descent of a submarine into an ocean starting from the surface is given in terms of descent t (time in seconds) by
dh/dt = 1 - (1 + t)^-2
where h is the depth of the submarine in metres

find an expression for h in terms of t (as a single fraaction) and hence find the depth of the submarine after 1 min.

answers:
h = (t^2)/(1+t)
59.0

i couldn't get the equation for h. my answer was always different....

(3) a particle is moving along the x axis. at time t, it is distant x from 0, and moving with velocity v = dx/dt
the acceleration of a body moving in a straight line is proportional to the velocity ie dv/dt = kv where k is a constant
when x =0 v = 7 and x = 3, v = 13
find the value of v when x = 2

Answer: (k = 2, v = 2x + 7) v = 11.


cheers

 

[wrxsti]

this is 3unit maths work
i would help you but im very tired.

hint : the last question should be a growth and decay eg) C = Ae^kt

 

[watatank]

the second question you just integrate dh/dt and make initial conditions t = 0, h = 0

 

[-pari-]

bump. c'mon guys

and watatank - yeah but my problem is i cant seem to get the integration bit right....

 

[vafa]

Solution:

View attachment 15470

 

[-pari-]

daym. why do i get the feeling you must be a maths teacher?

thanks! ^