Higher June 2019 Paper 6 Q17
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°.
Not to scale
(a) Aircraft A flies directly towards radar tower T at a speed of 890 km/h.
At what time will the aircraft pass over radar tower T?
Give your answer to the nearest minute. [4]
(b) Calculate the distance that was between aircraft A and aircraft B at 3pm. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6.39 [pm] or 1839 | 4 | B3 for 39 or answer rounding to 39.1 or 3°39 to 3°39′6.07″ or 6°39 to 6°39′6.07″ or 219 or answer rounding to 219.1 OR M1 for [\(t =\)] \(\dfrac{3250}{890}\) oe soi by 3.65(…) and M1FT for 60 × (their time) soi or evidence from their answer by using calculator key Alternative method (converting speed to km/min) M1 for 890 ÷ 60 soi by \(\dfrac{89}{6}\) or \(14\frac{5}{6}\) oe or 14.8[3…] and M1FT for [\(t =\)] 3250 ÷ their 14.8[3…] | Condone 1839pm for full marks e.g. \(3\frac{58}{89}\) their time could be fraction or decimal and could be just the non-integer part (check using calculator) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3345 to 3350 nfww | 4 | B1 for 42 seen AND M2 for [\(x^2 =\)] \(3250^2 + 4960^2 - 2 \times 3250 \times 4960 \cos\theta\) oe soi by [\(x^2 =\)] 11205110 to 11205111 or M1 for correct cosine rule with \(x^2\) not as subject Alternative method (using horizontal/vertical components and Pythagoras) M3 for \(\sqrt{(4960\sin 57 - 3250\sin 15)^2 + (3250\cos 15 - 4960\cos 57)^2}\) or M2 for 4960sin57 – 3250sin15 or 3250cos15 – 4960cos57 or M1 for two of 4960sin57, 3250sin15, 3250cos15 or 4960cos57 | May be seen on sketch diagram For M2 or M1, \(\theta\) is a number in the range \(15 \leqslant \theta \leqslant 57\) e.g. \(\cos\theta = \dfrac{3250^2 + 4960^2 - x^2}{2 \times 3250 \times 4960}\) Allow numerical values to imply relevant trig functions as below for M marks: 4960sin57 = 4159 to 4160 3250sin15 = 841 to 842 3250cos15 = 3139 to 3140 4960cos57 = 2701 to 2702 4960sin57 – 3250sin15 = 3317 to 3319 3250cos15 – 4960cos57 = 437 to 439 (4960sin57 – 3250sin15)² = 11 002 489 to 11 015 761 (3250cos15 – 4960cos57)² = 190 969 to 192 721 |