Two knights on horseback start from rest 88.0 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of .300 m/s^2, while Sir Alfred's has a magnitude of .200 m/s^2. Relative to sir Ggeorge's starting point, where do the knights collide?
The sum of the distances is 88m.
They collide at time t.
d=1/2 .300*t^2
88-d=1/2 .200 t^2
divide the second equation by the first will lead to this
88-d=d(2/3) solve for d
thanks
To find the location where the knights collide, we need to determine the time it takes for them to meet and then use that time to calculate their respective distances traveled.
Let's start by finding the time it takes for the knights to collide. We can use the equation:
\[ d = v_0 t + \frac{1}{2} a t^2 \]
Since both knights start from rest, \(v_0\) (initial velocity) for both of them is zero. Thus, the equation simplifies to:
\[ d = \frac{1}{2} a t^2 \]
For Sir George, with an acceleration of \(0.300 \, \text{m/s}^2\), the distance traveled is the starting point \(88.0 \, \text{meters}\). Plugging in the values:
\[ 88.0 = \frac{1}{2} \times 0.300 \, t^2 \]
Now let's solve for \(t\):
\[ t^2 = \frac{2 \times 88.0}{0.300} \]
\[ t^2 \approx 586.67 \]
\[ t \approx \sqrt{586.67} \]
\[ t \approx 24.00 \, \text{seconds} \]
Now that we know the time it takes for them to collide, we can calculate the distance traveled by Sir Alfred:
\[ \text{distance traveled by Sir Alfred} = v_0 \times t + \frac{1}{2} a \times t^2 \]
Since Sir Alfred also starts from rest, his initial velocity is zero. Plugging in the values:
\[ \text{distance traveled by Sir Alfred} = \frac{1}{2} \times 0.200 \times (24.00)^2 \]
\[ \text{distance traveled by Sir Alfred} \approx 115.20 \, \text{meters} \]
Finally, we can find the location of the collision relative to Sir George's starting point:
\[ \text{collision location} = 88.0 - \text{distance traveled by Sir Alfred} \]
\[ \text{collision location} = 88.0 - 115.20 \]
\[ \text{collision location} \approx -27.20 \, \text{meters} \]
Therefore, relative to Sir George's starting point, the knights collide approximately 27.20 meters before Sir George's position.