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MATH / A regular hexagon of side length 1 is placed vertically along one of its edges…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A regular hexagon of side length 1 is placed vertically along one of its edges on a flat surface. A particle is fired from the surface and passes through four of the vertices of the hexagon, as shown below, tracing the arc of a parabola. If the particle starts at AA and ends at B,B, then find the length AB.AB. [asy] unitsize(1.5 cm); real func (real x) { return(-2/sqrt(3)*x^2 + 7/(2*sqrt(3))); } pair A, B; A = (-sqrt(7)/2,0); B = (sqrt(7)/2,0); draw(shift((0,sqrt(3)/2))*(dir(240)--dir(180)--dir(120)--dir(60)--dir(0)--dir(-60))); draw((-2,0)--(2,0)); draw(graph(func,-sqrt(7)/2,sqrt(7)/2),red); label("AA", A, S); label("BB", B, S); [/asy]
Plain-text mathematical notation (without MathML)
A regular hexagon of side length 1 is placed vertically along one of its edges on a flat surface.  A particle is fired from the surface and passes through four of the vertices of the hexagon, as shown below, tracing the arc of a parabola.  If the particle starts at A and ends at B, then find the length AB.

[asy]
unitsize(1.5 cm);

real func (real x) {
  return(-2/sqrt(3)*x^2 + 7/(2*sqrt(3)));
}

pair A, B;

A = (-sqrt(7)/2,0);
B = (sqrt(7)/2,0);

draw(shift((0,sqrt(3)/2))*(dir(240)--dir(180)--dir(120)--dir(60)--dir(0)--dir(-60)));
draw((-2,0)--(2,0));
draw(graph(func,-sqrt(7)/2,sqrt(7)/2),red);

label("A", A, S);
label("B", B, S);
[/asy]
Original LaTeX notation
A regular hexagon of side length 1 is placed vertically along one of its edges on a flat surface.  A particle is fired from the surface and passes through four of the vertices of the hexagon, as shown below, tracing the arc of a parabola.  If the particle starts at $A$ and ends at $B,$ then find the length $AB.$

[asy]
unitsize(1.5 cm);

real func (real x) {
  return(-2/sqrt(3)*x^2 + 7/(2*sqrt(3)));
}

pair A, B;

A = (-sqrt(7)/2,0);
B = (sqrt(7)/2,0);

draw(shift((0,sqrt(3)/2))*(dir(240)--dir(180)--dir(120)--dir(60)--dir(0)--dir(-60)));
draw((-2,0)--(2,0));
draw(graph(func,-sqrt(7)/2,sqrt(7)/2),red);

label("$A$", A, S);
label("$B$", B, S);
[/asy]

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
46cfaa83-6bae-5782-835e-f9502bf46345
task_key
intermediate~5falgebra--test--46cfaa83-6bae-5782-835e-f9502bf46345
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import