In a historical movie, two knights on horseback start from rest 86 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. Relative to Sir George's starting point, where do the knights collide?

Relative to Sir George's starting point, the knights collide at a distance of 38.43 m from Sir George's starting point.

Explanation:

Let the distance covered by Sir George be

and the distance covered by Sir Alfred be

Since the knights collide, hence they must have traveled for the same amount of time just before collision

From one of the equations of motion for linear motion

Where is the distance traveled

is the initial velocity

is the acceleration

and is the time

For Sir George,

= 0 m/s (Since they start from rest)

0.21 m/s²

Hence,

becomes

Now, for Sir Alfred

= 0 m/s (Since they start from rest)

0.26 m/s²

Hence,

becomes

Since, they traveled for the same time, just before collision, we can write

Since, the two nights are 86 m apart, that is, the sum of the distances covered by the knights just before collision is 86 m. Then we can write that

m

Then,

Then,

becomes

m

∴ Sir George covered a distance of 38.43 m just before collision.

Hence, relative to Sir George's starting point, the knights collide at a distance of 38.43 m from Sir George's starting point.