In a historical movie, two knights on horseback start from rest 60 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.20 m/s2, while Sir Alfred's has a magnitude of 0.28 m/s2. Relative to Sir George's starting point, where do the knights collide?
They travel for the same time before colliding, so the distances covered before colliding are in a 0.28/0.20 = 1.4 ratio, if they maintain constant acceleration.
Alfred travels (1.4/2.4)* 60 = 35 m and George travels 25 m.
To determine where the knights collide, we need to calculate the time it takes for both knights to meet. Let's use the following steps:
Step 1: Determine the time for Sir George to reach the collision point:
We will use the equation of motion:
s = ut + (1/2)at^2
where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
For Sir George:
Given:
Initial velocity u = 0 m/s (starting from rest)
Acceleration a = 0.20 m/s^2
Distance s = 60 m
Rearranging the equation, we get:
s = (1/2)at^2
60 = (1/2) * 0.20 * t^2
120 = 0.10 * t^2
t^2 = 120 / 0.10
t^2 = 1200
t ≈ √1200
t ≈ 34.64 seconds (approx)
Therefore, it takes approximately 34.64 seconds for Sir George to reach the collision point.
Step 2: Determine the distance Sir George travels in that time:
Using the equation of motion:
s = ut + (1/2)at^2
For Sir George:
Given:
Initial velocity u = 0 m/s
Acceleration a = 0.20 m/s^2
Time t = 34.64 seconds (approx)
s = 0 * 34.64 + (1/2) * 0.20 * (34.64)^2
s = (1/2) * 0.20 * 1199.49
s ≈ 119.949 meters (approx)
Therefore, Sir George travels approximately 119.949 meters.
Step 3: Determine the distance Sir Alfred travels in 34.64 seconds:
In the same time it takes for Sir George to reach the collision point, let's calculate the distance Sir Alfred travels.
Given:
Initial distance between the knights = 60 m
Distance traveled by Sir George = 119.949 meters (approx)
Distance traveled by Sir Alfred = Initial distance - Distance traveled by Sir George
Distance traveled by Sir Alfred = 60 - 119.949
Distance traveled by Sir Alfred ≈ -59.949 meters (approx)
Since the distance traveled cannot be negative, we can conclude that Sir Alfred does not reach the collision point. Instead, he stops 59.949 meters behind his starting point.
Therefore, relative to Sir George's starting point, the knights collide approximately 119.949 meters away from it.