Question

In a historical movie, 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 0.300 m/s2 , while Sir Alfred’s has a magnitude of 0.200 m/s2 . Relative to Sir George’s starting point, where do the knights collide?

Answer 1

Let $L=88\ m$ is the distance between two knights before the start, $d$ is the distance from Sir George’s starting point to the point where the knights collide. Then, we can write the displacements of each knights:

$$d_G=\dfrac{1}{2}a_Gt^2=d,$$ $$d_A=\dfrac{1}{2}a_At^2=L-d.$$

Let's find $t^2$ from the first equation and plug it into the second one:

$$t^2=\dfrac{2d}{a_G},$$ $$\dfrac{1}{2}a_A(\dfrac{2d}{a_G})=L-d,$$ $$d(\dfrac{a_A}{a_G})=L-d.$$

Solving for $d$ we get:

$$d(\dfrac{a_A}{a_G}+1)=L,$$ $$d=\dfrac{L}{\dfrac{a_A}{a_G}+1},$$ $$d=\dfrac{88\ m}{\dfrac{0.2\ \dfrac{m}{s^2}}{0.3\ \dfrac{m}{s^2}}+1}=52.8\ m.$$

Answer:

$d=52.8\ m.$