Question 687424
An aircraft is flying horizontally at constant speed v at 1000 ft height.
When it is directly overhead a missile is fired vertically at constant speed 2v.
The missile constantly heads directly towards the aircraft.
How far will the missile have traveled when it hits the aircraft?
:
Let t = travel time of the plane and the missile from that point
then
vt = distance traveled by the plane
2vt = distance traveled by the missile
:
The missile will travel the hypotenuse of the right triangle formed by legs of
1000 ft and vt
:
(2vt)^2 = (vt)^2 + 1000^2
4v^2t^2 = v^2t^2 = 10^6
combine like terms
4v^2t^2 - v^2t^2 = 10^6
3v^2t^2 = 10^6
Find the square root of both sides
{{{sqrt(3v^2t^2)}}} = {{{sqrt(10^6)}}}
{{{vt*sqrt(3)}}} = 10^3
vt = {{{1000/sqrt(3)}}}, the distance traveled by the plane
then
{{{2(1000/sqrt(3))}}} = 1154.7 ft distance traveled by the missle