Question

In an historical movie, two knights on horseback start from rest 78.1 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.328 m/s2, while Sir Alfred's has a magnitude of 0.262 m/s2. Relative to Sir George's starting point, where do the knights collide?

Answer 1

Answer:

The answer is 43.418 [m]

Explanation:

See attachment to follow procedure

Steps:

1. Use linear movement equations to find final position, final velocities and time.

2. We know the final position of both knights will be the same, because they are colliding

3. We also know they will get to the final position at the exact same time, the only difference is that one of them will have covered more distance than the other one because of the higher acceleration.

From the above we know the following:

$x_{f} =x_{o} +vt+\frac{1}{2}at^{2}  \\v_{f} =v_{o} +at\\x_{1f} =x_{2f} =x_{f} \\t_{1} =t_{2}=t$

Writing equations for each knight and solving them, we will find the time it takes them to collide.

Taking this time and substituting in the equations we can get the final position for each knight which is the same and tells us where exactly they are colliding.

See the attachment to follow solving procedure.