Answer:
The knights collide 53.0 m from the starting point of sir George.
Explanation:
The equation for the position in a straight accelerated movement is as follows:
x = x0 + v0 t + 1/2 a t²
where
x = position at time t
x0 = initial position
v0 = initial speed
a = acceleration
t = time
The position of the two knights is the same when they collide. Since they start from rest, v0 = 0:
Sir George´s position:
xGeorge = 0 m + 0 m + 1/2 * 0.300 m/s² * t²
Considering the center of the reference system as Sir George´s initial position, the initial position of sir Alfred will be 88.0 m. The acceleration of sir Afred will be negative because he rides in opposite direction to sir George:
xAlfred = 88.0 m + 0 m - 1/2 * 0.200 m/s² * t²
When the knights collide:
xGeorge = x Alfred
1/2 * 0.300 m/s² * t² = 88.0 m - 1/2 * 0.200 m/s² * t²
0.150 m/s² * t² = 88.0 m - 0.100 m/s² * t²
0.150 m/s² * t² + 0.100 m/s² * t² = 88.0 m
0.250 m/s² * t² = 88.0 m
t² = 88.0 m / 0.250 m/s²
t = 18.8 s
At t = 18.8 s the position of sir George will be
x = 1/2 * 0.300 m/s² * (18.8 s)² = <u>53.0 m </u>
