DE problems help

1. Apr 15, 2013

uknowwho

4. A balloon is rising at the constant rate of 10 feet/second and is 100 feet from the ground at the instant when the astronaut drops his binoculars. (a) How long will it take the binoculars to strike the ground? (b) With what speed will the binoculars strike the ground?

so heres how i solved it:

a=-g
v=-gt + c1

v=0 and t=0

0=0 +c1
so c1=0

v=-gt

s=-gt^2/2 +c2

s=100 t=0

so 100=c2

s=-gt^2/2 + 100
s=-4.9t^2 + 100

putting s=0

-4.9t^2+100=0

getting t=4.5sec

and v=-44feet/sec

but the answer given at the back is t=2.83sec and v=80.62ft/sec

what am i doing wrong
When binoculars will be dropped at that time v will be zero and so will be the time and at the same time its distance from the ground will be 100feet

5. A projectile is fired vertically upward by a cannon with an initial velocity of vo meters per second.At what speed will the projectile be moving when it returns and strikes the hapless cannoneer(Neglect air resistance)

vi=v0 m/sec

acc=-g
v=-gt+c1
v0=c1
v=-gt+v0

s=-gt^2/2 + v0t + c2

s=0 and t=0

c2=0

s=-gt^2/2 +vot

s=-4.9t^2 + vot

how to solve it further?

9. Consider the differential equation dy/dt =k(A-y)(B+y) for the formation of trypsin in the small intestine.Assuming that A>B determing the time t at which trypsin is being formed most rapidly.

dy/dt=k(A-y)(B+y)

dy/dt+k(AB+Ay-By-y^2)

dy/dt=ABk +Aky_Bky-ky^2
dy/dt=ABk + k(A-B)y-ky^2

dy/k(A-B)y-ky^2=(ABk) dt

Im stuck here

2. Apr 15, 2013