What is the Width of the Car Based on Diffraction Limit Problem?

[grantaere]

Homework Statement

A child is standing at the edge of a straight highway watching her grandparents' car driving away at a constant 22.4 m/s. The air is perfectly clear and steady, and after 8.3 minutes the car's two taillights (654 nm) appear to merge into one. Assuming the diameter of the child's pupils is 4.76 mm, calculate the width of the car.

Homework Equations

Θ = 1.22 λ/D

The Attempt at a Solution

I solved for theta by plugging in the wavelength and diameter (came out to be 1.676 e -4 rad), then found the distance from the car using distance = time x speed = 11155.2m and multiplied that by the angle to find what I thought would be half the width of the car, and multiplied that by two to get an answer of 3.74m-- however, that's apparently incorrect and I'm not sure what I did wrong. Any help with be really appreciated. Thank you!

 

[Bystander]

... by the angle to find what I thought would be half the width ...

"Half?"

 

[grantaere]

"Half?"

Wouldn't the distance to the car be a line that forms a right triangle?

 

[Bystander]

Which tail-light of Grandmother's car is Little Red Riding Hood standing behind?

 

[grantaere]

Which tail-light of Grandmother's car is Little Red Riding Hood standing behind?

I assumed she's between the two, since it doesn't specify... would where she is change the answer??

 

[Bystander]

If she's standing behind one, how much further away could the other be?

 

[grantaere]

If she's standing behind one, how much further away could the other be?

Ahh, I see now- so I don't need to multiply by two because if she stands behind one light, the other is only 1.87m away. Thank you so much!