SOLUTION: 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

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 travelled when it hits the aircraft?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
=
= 10^3
vt = , the distance traveled by the plane
then
= 1154.7 ft distance traveled by the missle

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