# Math Help - How do I approach this question?

1. ## How do I approach this question?

Hi I am not sure how to approach this question and would like a nudge in the right direction and the general ideas around solving it.

Two helicopters set off from Hamilton airport at time t = 0. They follow the paths
r1(t) = (140t; 140t; 5t)
r2(t) = (200t; 0; 4t)
where t is measured in hours, and distances in kilometres. After a short flight, the first helicopter encounters problems and lands immediately on Pirongia at coordinates (28; 28; 1). Three minutes later, the second helicopter alters its course to rescue the occupants of the first helicopter. It flies in a straight line towards the landing site at 250kph. How long does it take for the second helicopter to get there?

2. Originally Posted by Vintex
Hi I am not sure how to approach this question and would like a nudge in the right direction and the general ideas around solving it.

Two helicopters set off from Hamilton airport at time t = 0. They follow the paths
r1(t) = (140t; 140t; 5t)
r2(t) = (200t; 0; 4t)
where t is measured in hours, and distances in kilometres. After a short flight, the first helicopter encounters problems and lands immediately on Pirongia at coordinates (28; 28; 1). Three minutes later, the second helicopter alters its course to rescue the occupants of the first helicopter. It flies in a straight line towards the landing site at 250kph. How long does it take for the second helicopter to get there?
1. Calculate the elapsed time which the 1st helicopter needs to reach the point L(28, 28, 1). You should come out with $t = \frac15\ h = 12\ min$

2. After 12 minutes the 2nd helicopter has reached the point H(40, 0, 0.8).

3. Calculate the distance between L and H:

$d=\sqrt{(28-40)^2+(28-0)^2+(1-0.8)^2} = \sqrt{928.04}$

4. From the definition of $speed = \dfrac{distance}{time}$ you know that $time = \dfrac{distance}{speed}$
You know the distance and the speed, calculate the necessary period of time.
Spoiler:
I've got 7 min 19 s

3. editEarboth beat me to it, and my answer was wrong :P