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MATH / An ant travels from the point A(0,−63) to the point B(0,74) as follows. It first crawls straight to (x,0) with x≥0, moving at a constant speed of √(2) units per second. It is then …

Problem

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problem

An ant travels from the point A(0,−63)A (0,-63) to the point B(0,74)B (0,74) as follows. It first crawls straight to (x,0)(x,0) with x≥0x \ge 0, moving at a constant speed of 2\sqrt{2} units per second. It is then instantly teleported to the point (x,x)(x,x). Finally, it heads directly to BB at 2 units per second. What value of xx should the ant choose to minimize the time it takes to travel from AA to BB?
Plain-text mathematical notation (without MathML)
An ant travels from the point A(0,−63) to the point B(0,74) as follows.  It first crawls straight to (x,0) with x≥0, moving at a constant speed of √(2) units per second.  It is then instantly teleported to the point (x,x).  Finally, it heads directly to B at 2 units per second.  What value of x should the ant choose to minimize the time it takes to travel from A to B?
Original LaTeX notation
An ant travels from the point $A (0,-63)$ to the point $B (0,74)$ as follows.  It first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second.  It is then instantly teleported to the point $(x,x)$.  Finally, it heads directly to $B$ at 2 units per second.  What value of $x$ should the ant choose to minimize the time it takes to travel from $A$ to $B$?

level

Level 5

type

Geometry

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Source and history

task_id
3c727641-bf18-56b3-9654-b7c0d0f15668
task_key
geometry--test--3c727641-bf18-56b3-9654-b7c0d0f15668
task_revision_id
1
config / split
geometry / test

Official source

initial import