Solving for Closest Approach: 2D Kinematics Help and Solutions

AI Thread Summary
A problem involving the 2D kinematics of two flocks of Canada geese flying at 25 km/hr is discussed, with one flock flying north and the other flying northwesterly. The key questions include finding the distance of closest approach, the time to reach this point, and the position vectors of both flocks relative to Kingston. Attempts to solve the problem involve setting up a distance formula and taking derivatives to find critical points. There are discrepancies in the calculations, prompting further review and corrections. The discussion emphasizes the need for accurate mathematical approaches in solving kinematic problems.
Kudo Shinichi
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Urgent!HELP!A problem on 2D kinematics

Homework Statement


A flock of Canada geese directly fly above Kingston is flying due north at a speed of 25km/hr. A second flock directly above Gananoque, 30km to the east of Kingston, is flying in a northwesterly direction at the same speed. Assume there is no wind where the geese are flying.
a)What is the distance of closest approach between the two flock
b)How long does it take to reach this point?
c)What are the position vectors of the two flocks relative to Kingston at this instant of time?

Can anyone help me? thank you very much.

The Attempt at a Solution


The formula for distance is ((30-25t/sqrt(2)) - 0)^2 + (25t - 25t/sqrt(2)) ^2 = 625t^2(3/2 - sqrt(2) + 1/4) -25 t sqrt(2) + 900
Derivative: 625t (3.5 - sqrt(2)) -25 sqrt(2). =0
t = 1/25(3.5 - sqrt(2)).
 
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Looks like the right approach.
Kudo Shinichi said:

The Attempt at a Solution


The formula for distance is ((30-25t/sqrt(2)) - 0)^2 + (25t - 25t/sqrt(2)) ^2
Looks good.
= 625t^2(3/2 - sqrt(2) + 1/4) -25 t sqrt(2) + 900
Redo this step. I get a different answer.
 

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