Question from Past Paper (1 Viewer)

[Dreamerish*~]

At 9 am, an ultralight aircraft flies directly over Daryl's head at 500 metres. It maintains a constant speed of 20ms^-1 and a constant altitude. If x is the horizontal distance travelled by the plane and θ is the angle of elevation from Daryl to the plane,

i) Show that dx/dθ = -500cosec²θ

ii) Hence, show that dθ/dt = -(sin²θ)/25

iii) Find the rate of change of the angle of elevation at 9:01 am.

I'm okay with i), but can't figure out ii) and hence iii).

 

[FinalFantasy]

At 9 am, an ultralight aircraft flies directly over Daryl's head at 500 metres. It maintains a constant speed of 20ms^-1 and a constant altitude. If x is the horizontal distance travelled by the plane and θ is the angle of elevation from Daryl to the plane,

i) Show that dx/dθ = -500cosec²θ

ii) Hence, show that dθ/dt = -(sin²θ)/25

iii) Find the rate of change of the angle of elevation at 9:01 am.

I'm okay with i), but can't figure out ii) and hence iii).

i) tan θ=500\x

x=500\tanθ=500cotθ
dx\dθ=-500cosec²θ bcoz d\dx(cotx)=-cosec²x

ii)dθ\dt=dθ\dx*dx\dt
using "It maintains a constant speed of 20ms-1"
dx\dt=20
so dθ\dt=-sin²θ \500 times 20
=-sin²θ\25

iii)rate of change of angle of elevation is dθ\dt
at 9:01am 1minute has passed, dats 60 seconds
get θ in terms of t and den put in the t=60 and den put back θ into ur dθ\dt

 

[Dreamerish*~]

Oh!

So if dx/dθ = a/b, then dθ/dx = b/a?

Thank you very much.

 

[FinalFantasy]

ya u juz invert it as long as it's a whole
but when it's not a whole thing u gota make it a whole thing first
e.g
dx\dt=a\c+b\d
dt\dx is NOT c\a+d\b
u have to make it as a whole thing first

 

[shafqat]

You can treat those limits just like normal fractions.

 

[who_loves_maths]

Originally Posted by FinalFantasy
ya u juz invert it as long as it's a whole
but when it's not a whole thing u gota make it a whole thing first
e.g
dx\dt=a\c+b\d
dt\dx is NOT c\a+d\b
u have to make it as a whole thing first

lol, year 7 arithmetic FF?
i'm sure Dreamerish*~ already knew the above fact

 

[FinalFantasy]

hahaha o wellz juz ignore me if u already know dat