Solving for Closest Approach: 2D Kinematics Help and Solutions

[Kudo Shinichi]

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)).

 

[Doc Al]

Looks like the right approach.

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.

 

[baba89]

a) The distance of closest approach is the minimum distance between the two flocks, which occurs when t=1/25(3.5 - sqrt(2)). Plugging this value back into the distance formula, we get a minimum distance of approximately 18.3 km.

b) To find the time it takes to reach this point, we can plug in the value of t into the time formula, t = d/v. We know the distance (18.3 km) and the speed (25 km/hr), so the time it takes to reach this point is approximately 0.732 hours, or 43.9 minutes.

c) The position vectors of the two flocks relative to Kingston at this instant of time can be found by plugging in the value of t into the position vector formulas, x = x0 + v0t and y = y0 + v0t. Since both flocks are flying due north, the x coordinate of their position vectors will be 0. For the flock above Kingston, the y coordinate will be 25t, and for the flock above Gananoque, the y coordinate will be 30-25t/sqrt(2). Plugging in the value of t, we get the position vector for the flock above Kingston as (0, 0.732) and the position vector for the flock above Gananoque as (0, 2.142). These position vectors represent the distance (in km) from Kingston to the flocks at the closest approach point.