In a historical movie, two knights on horseback start from rest 91 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.18 m/s2, while Sir Alfred's has a magnitude of 0.33 m/s2. Relative to Sir George's starting point, where do the knights collide?
use
u=initial velocity=0 m/s
a=acceleration, m/s²
t=time in seconds
Distance S = ut+(1/2)at² m
for each knight.
The sum of the distances is 91 m.
Solve for t and hence the distances travelled by each.
i still don't understand how to write this equation
To determine where the knights collide, we need to find the time it takes for them to meet. We can do this by calculating the time for each knight to accelerate from rest to the point of collision.
First, let's find the time it takes for Sir George to reach the collision point. We can use the equation:
v = u + at,
where:
- v is the final velocity,
- u is the initial velocity (0 m/s since Sir George starts from rest),
- a is the acceleration of Sir George (0.18 m/s²),
- t is the time taken.
Since Sir George's final velocity at the point of collision is the same as Sir Alfred's, we can write:
v = 0.33 m/s² * t.
Setting the two expressions for v equal to each other:
0.33 m/s² * t = 0.18 m/s² * t,
Rearranging the equation gives us:
0.33 m/s² * t - 0.18 m/s² * t = 0.
Now we can solve for t:
0.15 m/s² * t = 0.
Since the left side of the equation is zero, we can't determine the exact value of t. However, this implies that the time taken for Sir George to reach the collision point is infinite. This occurs because Sir George's acceleration is lower than Sir Alfred's, so he will never catch up to him.
Therefore, the knights will not collide, and they will continue riding indefinitely without a battle.