Saturday

August 30, 2014

August 30, 2014

Posted by **Michael** on Thursday, November 11, 2010 at 9:21pm.

- Related rates -
**Reiny**, Thursday, November 11, 2010 at 9:43pmAt a time of t hours

let the distance covered by the eastbound person be 1t km

let the distance covered by the northeastbound person be 2t km

let the distance between them be d km

by the Cosine Law

d^2 = t^2 + 4t2 - 2(t)2t)cos45°

= 5t^2 - 4t^2(√2/2)

= 5t^2 - 2√2 t^2

when t = 15 min or .25 hours

d^2 = 5(.25)^2 - 2√2(.25)^2 = .489277

d = .6995

2d dd/dt = 10t -4√2t

dd/dt = (5t - 2√2t)/d

= (5(.25) - 2√2(.25))/.6995 = .776

at that moment they are separating at .776 km/h

check my arithmetic

- Related rates -
**Michael**, Thursday, November 11, 2010 at 9:55pmIncorrect

- Related rates -
**Reiny**, Thursday, November 11, 2010 at 10:08pmIf you had checked my arithmetic like I suggested you would have found my error to be in

d^2 = 5(.25)^2 - 2√2(.25)^2 = .489277

It should have been

d^2 = 5(.25)^2 - 2√2(.25)^2 =**.135723**

then

d =**.3684**

I will let you make the rest of the corrections.

BTW, I also used km/h instead of mi/h, but that has no effect on the calculation

**Related Questions**

calculus - Two people start from the same point. One walks east at 3 mi/h and ...

Calculus - Two people start from rest at the same point. One walks east at 3 mi/...

Calculus - Two people start from the same point. One walks east at 5 mi/h and ...

calculus - Could someone help me et up this problem? Two people start from the ...

Math: Compass Bearings - two people start walking from the same point. Person A ...

Math - A man walks one mile east, then he walks one mile northeast and then he ...

calculus - Two cars start from the same point at the same time. One travels ...

Math (Trigonometry) - Jasper walks 2 km due east. He then turns and walks 3 km ...

physics - a woman walks 2 km due east and then walks 4 km in the direction 30 ...

maths - a hiker walk due east at 4km per hour and a second hiker starting from ...