2 cars passing

bobbixler

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Feb 9, 2012
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2 cars are approaching each other in the same lane and about to have a head on collision. You are in the first car when you first see the approaching car 500 ft. away traveling toward you at 88 feet per second. You immediately steer to the right as hard as you can without losing control. You do not brake. Assume that the radius of your turn (in feet) is (V^2)/23 where V is your velocity in feet per second. What velocity should you be driving in order to maximize the distance between your car and the other car as you pass?
 
2 cars are approaching each other in the same lane and about to have a head on collision. You are in the first car when you first see the approaching car 500 ft. away traveling toward you at 88 feet per second. You immediately steer to the right as hard as you can without losing control. You do not brake. Assume that the radius of your turn (in feet) is (V^2)/23 where V is your velocity in feet per second. What velocity should you be driving in order to maximize the distance between your car and the other car as you pass?

I think you're supposed to assume the turn is a "hard" right and that your direction of travel (immediate right) is perpendicular to the oncoming car's direction.

if you let driver 1's perpendicular distance (radius) = "r" and velocity of driver 1 (velocity of radius) = V = dr/dt, you can isolate r and dt by using the given relationship r = V2/23 and substituting V = dr/dt

Once you have an explicit relationship of the radius (perpendicular distance travelled by driver 1) then you know the distance of the second driver is just -88t + 500

so the square of the distance between both drivers is just (r2) + (-88t + 500)2

where r is also a function of t, becasue both functions are parrallel to each other the distance between either driver is just the hypoteneuse of the triangle formed by both functions at any given time t.

EDIT:

im not too sure about this acutally since the distance (between the two cars) formula give a positive quadratic, which has no minimum value.:???:
 
Last edited:
to clarify

Your turn to the right is not perpendicular to the oncoming car. It is an arc of a circle with the radius as specified.
 
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