Knights' Collision: Solving a 1D Kinematics Problem for Homework

[Neil6790]

Homework Statement

In a historical movie, two knights on horseback start from rest 62 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.21 m/s2, while Sir Alfred's has a magnitude of 0.26 m/s2. How far from Sir George's starting point do the knights collide?

Homework Equations

The Attempt at a Solution

62 - x = (1/2)*(0.21 m/s^2)t^2
62 - x = (1/2)*(0.26 m/s^2)t^2

I was trying to find any velocity or any time but i can't seem to conceive anything logic that would work. Any help would be greatly appreciated.

 

[danago]

Try to write equations that give the position of each knight relative to Sir George's starting position at any given time, and then find when they are equal.

 

[LowlyPion]

Homework Statement

In a historical movie, two knights on horseback start from rest 62 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.21 m/s2, while Sir Alfred's has a magnitude of 0.26 m/s2. How far from Sir George's starting point do the knights collide?

Homework Equations

The Attempt at a Solution

62 - x = (1/2)*(0.21 m/s^2)t^2
62 - x = (1/2)*(0.26 m/s^2)t^2

I was trying to find any velocity or any time but i can't seem to conceive anything logic that would work. Any help would be greatly appreciated.

Almost the right idea.
You need to use different X1 and x2

X₁ = 1/2a₁t²

X₂ = 1/2a₂t²

You know that they meet by definition when the time is equal and ...their total distance adds to 62.

Divide the first equation by the second.

You get X₁/X₂ = a₁/a₂

and you know X₁ + X₂ = 62.