If an object in the shape of a rectangle with the length of 2520 km and width of 1650 km, with a rotation of 24°53’24’', moving at half the speed of light, losing 34.56% of its speed every second, starting from the left-most point on the object touching point A, takes 45.23 seconds for the right-most point on the object to reach point B, how far away are the 2 points?
The object’s length (2520 km) and its orientation don’t directly impact the calculation of distance between points A and B, given the information provided.
The object’s speed and deceleration are crucial.
Initial speed = 0.5c (half the speed of light)
Deceleration = 34.56% per second
Let’s calculate the distance traveled by the right-most point of the object:
Convert initial speed to km/s: 0.5c ≈ 149,896.229 km/s
Calculate the distance traveled in 45.23 seconds, considering deceleration:
We’ll use the formula for distance under constant acceleration (or deceleration):
d = v0 * t + (1/2) * a * t^2
However, since the deceleration is given as a percentage, we’ll calculate the average speed over the time period.
Average speed = (initial speed + final speed) / 2
To find the final speed, we’ll calculate the speed at each second and then find the average.
Let’s simplify the calculation:
Calculate the final speed after 45.23 seconds:
Speed reduction per second = 34.56%
Final speed = 149,896.229 km/s * (1 - 0.3456)^45.23 ≈ 0 km/s (due to rapid deceleration)
Given the rapid deceleration, the object would likely come to a stop before 45.23 seconds. Let’s estimate the average speed:
d = average speed * time ≈ 74,948.1145 km/s * 45.23 s ≈ 3,390,911 km
However, this calculation assumes constant deceleration and average speed. Given the complexity and rapid deceleration, this approximation might not be entirely accurate.
Considering the object’s length (2520 km), if the left-most point starts at point A, and the right-most point reaches point B after 45.23 seconds, the distance between points A and B would be approximately:
Distance ≈ d - object’s length ≈ 3,390,911 km - 2520 km ≈ 3,388,391 km
Keep in mind that this calculation involves approximations due to the complexity of the problem.
I assume they meant the object is moving along the line with the given angle from the object, therefore, to find the actual distance between A and B, you do need to take into account the orientation of the object to find both the longitudinal distance along the movement path and the transverse distance between the two corners of the rectangle. You’ll then need to find the final distance by using Pythagoras theorem.
Thats too easy of a question
Solution:
Initial speed = 0.5c (half the speed of light) Deceleration = 34.56% per second
Let’s calculate the distance traveled by the right-most point of the object:
We’ll use the formula for distance under constant acceleration (or deceleration):
d = v0 * t + (1/2) * a * t^2
However, since the deceleration is given as a percentage, we’ll calculate the average speed over the time period.
Average speed = (initial speed + final speed) / 2
To find the final speed, we’ll calculate the speed at each second and then find the average.
Let’s simplify the calculation:
Speed reduction per second = 34.56% Final speed = 149,896.229 km/s * (1 - 0.3456)^45.23 ≈ 0 km/s (due to rapid deceleration)
Given the rapid deceleration, the object would likely come to a stop before 45.23 seconds. Let’s estimate the average speed:
Average speed ≈ (149,896.229 km/s + 0 km/s) / 2 ≈ 74,948.1145 km/s
Now, calculate the distance:
d = average speed * time ≈ 74,948.1145 km/s * 45.23 s ≈ 3,390,911 km
However, this calculation assumes constant deceleration and average speed. Given the complexity and rapid deceleration, this approximation might not be entirely accurate.
Considering the object’s length (2520 km), if the left-most point starts at point A, and the right-most point reaches point B after 45.23 seconds, the distance between points A and B would be approximately:
Distance ≈ d - object’s length ≈ 3,390,911 km - 2520 km ≈ 3,388,391 km
Keep in mind that this calculation involves approximations due to the complexity of the problem.
I assume they meant the object is moving along the line with the given angle from the object, therefore, to find the actual distance between A and B, you do need to take into account the orientation of the object to find both the longitudinal distance along the movement path and the transverse distance between the two corners of the rectangle. You’ll then need to find the final distance by using Pythagoras theorem.
It’s a copy/pasted answer from a LLM. I think relativistic effects would be significant, too
Wouldnt the relativistic effect only matter if i specified the point of reference?
Also, the approximation is terrible
Nah man the reason won’t arrive, reasons don’t run on roads.