Two helicopters take off simultaneously from airfields A and B, which are 500 km apart. After 1 hour and 20 minutes from their meeting point, the helicopter originating from airfield A lands at airfield B. The second helicopter lands at airfield A 3 hours after the meeting. Determine the speed of both helicopters.

Question

12-02-2025
Physics

High School

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Two helicopters take off simultaneously from airfields A and B, which are 500 km apart. After 1 hour and 20 minutes from their meeting point, the helicopter originating from airfield A lands at airfield B. The second helicopter lands at airfield A 3 hours after the meeting. Determine the speed of both helicopters.

Answer :

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nazmalik855 nazmalik855 · Answer 1 · 2024-04-12T01:57:33-04:00

Final Answer:

The speed of the helicopter originating from airfield A is \[tex](375 \, \text{km/h}\),[/tex] and the speed of the helicopter originating from airfield B is[tex]$250 \, \text{km/h}$.[/tex]

Explanation:

Let (x) be the speed of the helicopter from airfield A and (y) be the speed of the helicopter from airfield B.

The helicopter from airfield A travels for 1 hour and 20 minutes, covering a distance of[tex]$1 \, \text{hour} \times x + \frac{1}{3} \, \text{hour} \times y$[/tex], which is equal to the distance between the airfields. Similarly, the helicopter from airfield B travels for 3 hours, covering a distance of [tex]$3 \, \text{hours} \times y$[/tex], which is also equal to the distance between the airfields.

So, we have the equation:

[tex]\[1x + \frac{1}{3}y = 500\]\[3y = 500\][/tex]

Solving these equations simultaneously, we find[tex]$x = 375 \, \text{km/h}$ and $y = 250 \, \text{km/h}$.[/tex]

Therefore, the speed of the helicopter originating from airfield A is[tex]$375 \, \text{km/h}$[/tex], and the speed of the helicopter originating from airfield B is [tex]$250 \, \text{km/h}$.[/tex]

In conclusion, by setting up and solving equations based on the distances covered by each helicopter, we determine the speeds of the helicopters from airfields A and B as [tex]$375 \, \text{km/h}$ and $250 \, \text{km/h}$,[/tex] respectively.