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An aeroplane flies horizontally at 150 m s⁻¹ along a bearing 60° east of north - AQA - A-Level Physics - Question 22 - 2022 - Paper 1

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An aeroplane flies horizontally at 150 m s⁻¹ along a bearing 60° east of north. How far north from its starting position is the aeroplane after one hour? A 270 km ... show full transcript

Worked Solution & Example Answer:An aeroplane flies horizontally at 150 m s⁻¹ along a bearing 60° east of north - AQA - A-Level Physics - Question 22 - 2022 - Paper 1

Step 1

Calculate the time elapsed after one hour

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Answer

The time the aeroplane has flown is 1 hour. To convert this into seconds:

t = 1 ext{ hour} = 3600 ext{ seconds}.

Step 2

Calculate the northward distance traveled

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Answer

The aeroplane flies at a speed of 150 m/s. Thus, the total distance traveled in one hour is:

d = ext{speed} imes ext{time} = 150 ext{ m/s} imes 3600 ext{ s} = 540000 ext{ m}.

To find the northward component, we use the angle 60°:

d_{north} = d imes ext{cos}(60°) = 540000 ext{ m} imes 0.5 = 270000 ext{ m}.

Converting this to kilometers gives:

d_{north} = 270 ext{ km}.

Step 3

Select the correct answer from the options

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Answer

From the calculations, the distance traveled north is 270 km. Therefore, the correct answer is:

A 270 km.

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