What is the Minimum Distance Between a BMW and a Camper to Avoid Collision?

[jojo711]

Homework Statement

Suppose that a man driving a BMW zooms out of a darkened tunnel at 39.2 m/s. He is momentarily blinded by the sunshine. When he recovers, he sees that he is fast overtaking a camper ahead in his lane moving at the slower speed of 15.7 m/s. He hits the brakes as fast as he can (his reaction time is 0.26 s). If he can decelerate at 3.5 m/s2, what is the minimum distance between the driver and the camper when he first sees it so that they do not collide?

Homework Equations

V=Vo+at
X=Xo+volt+1/2at^2
V^2=Vo^2+2a(X-Xo)

The Attempt at a Solution

I took the second equation and plugged in the numbers [V=39.2(0.26)+1/2(3.5)(0.26^2)] and ended with the answer being 10.3103. When I put my answer in, it was wrong. Please help me!

 

[gneill]

Homework Statement

Suppose that a man driving a BMW zooms out of a darkened tunnel at 39.2 m/s. He is momentarily blinded by the sunshine. When he recovers, he sees that he is fast overtaking a camper ahead in his lane moving at the slower speed of 15.7 m/s. He hits the brakes as fast as he can (his reaction time is 0.26 s). If he can decelerate at 3.5 m/s2, what is the minimum distance between the driver and the camper when he first sees it so that they do not collide?

Homework Equations

V=Vo+at
X=Xo+volt+1/2at^2
V^2=Vo^2+2a(X-Xo)

The Attempt at a Solution

I took the second equation and plugged in the numbers [V=39.2(0.26)+1/2(3.5)(0.26^2)] and ended with the answer being 10.3103. When I put my answer in, it was wrong. Please help me!

Your chosen equation does not address the problem as stated. The 0.26s time span is the driver's reaction time -- the time between when he recognizes the danger and when he actually does something about it. No braking is happening during that time! No velocity change is taking place during that time!

You'll have to consider the problem in two parts: the 'reaction time phase' and the 'braking phase'.

 

[LawrenceC]

Hint: The speed of the BMW must just equal the speed of the camper just the split second it catches it. That defines a time.

As an aside, the brakes on the BMW are not working properly. The average vehicle has an acceleration rate under maximum braking of -1g which is -9.8 m/s^2.