Application of Calc. Question (1 Viewer)

totallybord

Member
Joined
Mar 13, 2006
Messages
209
Gender
Female
HSC
2008
Hi,
Help!
At noon a truck leaves Sydney dirving west at a speed of 40km/h. An hour later a 2nd truck leaves Sydney driving south at a speed of60km/h. At what rate is the distance btwn the 2 trucks increasing at 2pm that day?

Thanks for any help:D
 

lyounamu

Reborn
Joined
Oct 28, 2007
Messages
9,989
Gender
Male
HSC
N/A
totallybord said:
Hi,
Help!
At noon a truck leaves Sydney dirving west at a speed of 40km/h. An hour later a 2nd truck leaves Sydney driving south at a speed of60km/h. At what rate is the distance btwn the 2 trucks increasing at 2pm that day?

Thanks for any help:D
What's the answer. Can you post it up. I want to see if I got it right. Then, I can post up my solution.

I will just do this:
Let x be the horizontal line and y be the vertical line and z between them.

So we have a right-angled triange.

dx/dt = 40 so x = 40t + 40 as this truck leaves an hour earlier so it already covered 40km
dy/dt = 60 so y = 60t (for this one, constant is zero because it starts from the origin)

For this question, we will be substituting t = 1 instead of 2 as the whole working-out has been adjusted to the car that is heading south, not the car that is going west.

z^2 = x^2 + y^2
= (40t+40)^2 + (60t)^2
= 1600t^2 + 3200t + 1600 + 3600t^2
= 5200t^2 + 3200 t + 1600
z = square root of (5200t^2 + 3200t + 1600)
dz/dt = 1/2 . 1/square root of (5200t^2 + 3200t + 1600) . (10400t + 3200) (substitute t = 1 here instead of t=2 as I adjusted the whole working-out for the car that went towards south, not the car that went west)
So dz/dt = 68km/h

I hope I am right...
 
Last edited:

3unitz

Member
Joined
Nov 18, 2006
Messages
161
Gender
Undisclosed
HSC
N/A
right angled triangle 40t in x direction, (60t - 60) in y direction (note: wont work for t < 1)

D = [(60t - 60)^2 + (40t)^2]^(1/2) from pythagoras

dD/dt = (1/2)[(60t - 60)^2 + (40t)^2]^(-1/2) . {[2(60t - 60)].60 + 2(40t).40}

sub t = 2,

R = (1/2)(3600 + 6400)^(-1/2) . (7200 + 6400)

R = 68 km/h
 

totallybord

Member
Joined
Mar 13, 2006
Messages
209
Gender
Female
HSC
2008
yep the answer is 68km/h! thanks for the help!!
3unitz: why is it 60t-60?
 

lyounamu

Reborn
Joined
Oct 28, 2007
Messages
9,989
Gender
Male
HSC
N/A
totallybord said:
yep the answer is 68km/h! thanks for the help!!
3unitz: why is it 60t-60?
It left 1 hour later which means that I didn't cover 60km earlier.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top