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17 T is a radar tower - OCR - GCSE Maths - Question 17 - 2019 - Paper 6
Question 17
17 T is a radar tower. A and B are two aircraft. At 3pm • aircraft A is 3250 km from T on a bearing of 015°. • aircraft B is 4960 km from T on a bearing of 057°.... show full transcript
Worked Solution & Example Answer:17 T is a radar tower - OCR - GCSE Maths - Question 17 - 2019 - Paper 6
Step 1
Calculate the time aircraft A will take to reach radar tower T
Answer
To find the time taken for aircraft A to fly towards radar tower T, we first need to calculate the straight line distance from aircraft A to tower T, which is 3250 km.
Using the formula:
ext{Time} = rac{ ext{Distance}}{ ext{Speed}}Substituting the values gives:
ext{Time} = rac{3250 ext{ km}}{890 ext{ km/h}} \ = 3.6483... ext{ hours} \ \approx 3 ext{ hours and } 39 ext{ minutes} \ \approx 3 ext{ hours and } 39 ext{ minutes or } 219 ext{ minutes}.Hence, aircraft A will pass over radar tower T at around 6:39 pm.
Step 2
Calculate the distance between aircraft A and aircraft B at 3pm
Answer
To find the distance between aircraft A and B at 3pm, we can use the cosine rule. The positions of the aircraft create a triangle with:
- side a = 3250 km (distance from T to aircraft A)
- side b = 4960 km (distance from T to aircraft B)
- angle C = 057° - 015° = 42° (the angle between the two positions).
Applying the cosine rule:
Substituting in the values gives:
Calculating each part, we find:
ext{c}^2 = 10562500 + 24601600 - 2 imes 3250 imes 4960 imes 0.7431 \ = 10562500 + 24601600 - 2 imes 3250 imes 4960 imes 0.7431 \ \ = 10562500 + 24601600 - 2 imes 16155.7408 \ = 10562500 + 24601600 - 64313.496 \ \ = 30564100 - 64313.496 \ \ = 30500000.504\Finally:
Thus, the distance between aircraft A and B at 3pm is approximately 3480 km.