0 Leavin Certificate Applied Maths Hiher Level Answers ) (a) (b) (i) r (ii) d (iii) m ) (a) 0 m s - 9 N of E ) (b) (i) km h - 0 S of E (ii) (iii) 90 km ) (a) (i) 0 6 (ii) h 0h s s ) (a) (i) 8 m N (ii) 006 m (iii) 6 m N (b) (ii) ) (a) (i) m s (ii) 6 (b) (i) 0v (ii) 0 cos m 6) (a) : (b) (ii) m ) (a) 9 N @ 9 N 8) (b) (i) 69ma (iii) 0 9) (a) 9 cm (b) (i) 00 m (ii) 99 cm 0 0) (a) (i) t e (ii) 0 s 0 m (b) (ii) 06 ) (a) (ii) m s - (iii) 0 m ) (a) (i) km h - (ii) E of N 9 E of N (b) (i) 0 s (ii) 8 s ) (a) (i) s (ii) 06 m (iii) 09 m s - (b) 0 ) (a) (i) 9 m s - 8 m s - (ii) 0 m s - ) (b) (i) 6 N (ii) 090 s ) (a) (ii) 0 m s - 0 m s - (iii) (b) (i) i j i j (ii) 6) (a) (i) 990 m s - (ii) 80 (b) (ii) m s - (iii) 0 s 8) (b) (i) 88 k m (ii) 9 J (iii) m M 9) (a) h (b) s 0) (a) (ii) 0 m (b) (i) v A (ii) Asin t d 0 ) (a) m (b) (i) s (ii) 886 m ) (a) (i) 9 km h - 9 N of W (ii) 6 m (b) (i) 80 m s - 9 ) (a) (i) or -0 (ii) 0 s or 0 s (iii) 0 m ) (a) (i) 9 m s - (ii) m s - (iii) m s - ) (b) (i) 00 m s - (ii) 0 N ) (a) (ii) 9 80u 8R m 6) (a) (i) d (ii) d (b) 6 W c l ) (a) (i) (ii) W 9 l c (b) (i) W W (iii) 06 8) (b) (i) (ii) c c 9) (a) 866 k m - (b) (i) 88 (ii) 06 m 0) (a) (i) 6 m s - (ii) 6 m (b) (i) F 0 00 (ii) 800 (iii) 69 0 ) (a) (i) t m (iii) s (ii) 8 m (b) (i) 0 m s - (ii) m s - ) (a) (i) 8:00 (ii) 8: ) (b) (i) km hr - (ii) 9 km ) (a) 8 m s - ) (a) (i) 9 m s - (ii) 096 N (b) (ii) ) (a) (ii) s 0 m 0 mu (b) (i) 08 (ii) 69 6) (a) (i) 8 N 8 m- (ii) N (b) (i) d (ii) 06m r ) (a) (i) cm cm (ii) 69 (b) (ii) 06 (iii) N 00 8) (b) (i) (ii) 9) (a) 00 k m - 800 k m - (b) (i) (ii) 60 N (iii) 86 k m - 0) (a) (i) m s - (ii) 0 m (b) (i) s s (ii) t t t (iii) m 0 ) (a) s ) (a) (i) 6 m (ii) (b) W 60 S ) (a) (ii) 0 (b) ) (a) (i) 8 N (ii) 89 mm m u u N (b) ) (a) (i) e e (ii) 6 m m m m m m 8 8 ) (b) (i) (ii) (iii) cm 6) (a) (i) 09 (ii) s W b W b ) (a) 68 (b) (i) (b) (i) ml ml (ii) 6l r 8) (b) (i) (ii) r 9) (a) 0000 m 0000 m (b) 00 0) (a) (b) (i) 60 m s - 6 m (ii) 0 s (c) 9 mins Dominick Donnelly wwwappliedmathematicsie 0 Pae
0 ) (a) m (b) (i) 0 s (ii) m ) (a) 8 (b) (i) km hr - at 6 E of N (ii) : (iii) hr 9 min ) (a) (i) 69 & (ii) s (b) (i) 60 (ii) 0 m s - ) (a) (i) m (ii) m (b) (i) (ii) f 6) (a) (i) m s (ii) 9 N (b) (i) m s - (ii) 09 ) (a) 6 8) (b) (i) mi (ii) 8m I mr 9) (a) 9 (b) (i) m (ii) 60 0) (a) (i) 000 (ii) 8 0 ) (a) s (b) (ii) t 8 t t (iii) t ) (a) (i) 6 m s at 89 S of W (ii) 96 m (b) 89 60 ) (a) (i) 0 (ii) 6 (b) (i) 6 (ii) ) (a) m s- (b) N 9 N N ) (a) (ii) ¼ < e < (b) (i) e (ii) ¾ 6) (a) (ii) 6 m rad s - 09 rad (b) rad s - ) (a) (ii) 800 N m - 8) (b) (i) 9 rad s - (ii) s 0 m 9) (a) 88 0-6 m (b) 0) (a) 66 (b) (i) 6 m (ii) 9 m s- 00 ) (a) (i) - m s - (ii) (b) 00 m ) (a) (i) m 6 s ) (a) 9 m (b) (i) (ii) ) (a) (i) 6) (b) (i) u e u e 8 m s at 8 S of E (b) m s - from East 0 m s ) (a) (i) N (ii)08 m s - (b) (ii) (ii) 0% (b) (i) k 6) (a) (i) k a a m s (ii) ⅔ s ) (b) (ii) W (iii) W 8) (b) (ii) 9) (b) (i) (ii) W 0) (a) y e (b) (i)8 m s - (ii) s 9 009 ) (b) (ii) ) (a) (i) 60 m (ii) 8 m 96 m (b) ) (a) (i) m/s (ii) m (b) (i) mm m m m m ut b m s (ii) m s 8 m s 9) (a) 0 k m - cos u 6 ) (a) (i) 0 0 s N (ii) ) (a) (i) u e u e (iii) ⅓ 900 W ) (b) (ii) N 80 W of N (iii) % 6) (a) (ii) 0 cm/s (b) ) (a) cm (b) N 8) (b) (i) 6ml (ii) 9) (a) 8 cm (b) (i) s l (ii) W 0) (a) y (b) (i) k (ii) 008 ) (a) (i) s (ii) 8 m (b) (i) m/s m/s (ii) 8 m/s (iii) m ) (a) (i) m/s S of E (ii) 6 m (b) from 6 W of N ) (b) ) (b) (ii) ) (a) (i) e e e 6) (a) (ii) 68 m/s 08 m/s (b) 9 ) (a) (b) 8) (b) (i) 6 (ii) 9 N N 9) (a) 06 m (b) (i) 08 (ii) 0 N (iii) 8 cm 0) (a) (b) (i) 00 (ii) 0 m/s Dominick Donnelly wwwappliedmathematicsie 0 Pae
00 ) (a) (i) m/s (ii) 00 m (b) (ii) ) (a) (i) 0 km/hr N of E (ii) mins (b) 80 m ) (a) ) (a) s 8m (b) (ii) T ) (a) (i) v 6 e v 6 e (b) (i) usin ucos (ii) 90 m 8 d W 6) (b) (iii) u cos 6) (a) (ii) ) (a) (b) (ii) 80 N 8) (b) (i) (ii) 8 m/s 0 9) (a) cm (b) (i) 0 (ii) 00 k 0) (a) 006 ) (a) (ii) d ft 8 (b) (i) t + 0t 0t + 0t (ii) 6 s (iii) s ) (a) (i) 6 km/hr (ii) 88 km/hr West (b) (i) 8 m m (ii) (iii) m ) (a) (i) r 98t i 9 t t j v 98i 9t t j (ii) tan t y cos (b) (i) m/s (ii) 6 m s - (iii) s s (b) ) (a) (i) m/s (ii) 00 s (b) (iii) 0 ) (a) (i) e e u u (ii) (b) (i) e e e 9 6) (a) (i)8 m/s (ii) s (b) 0 m ) (a) (i) 6 N (ii) 6 N 68 (b) λ 8) (b) (i) rad/s (ii) m N 9) (a) (i) 06 cm 000 a e (ii) 6 (b) (i) 0) (a) y (b) (i) 066 m/s (ii) s 00 ) (a) (i) m (ii) m (b) (i) 98 N (ii) 0 m ) (a) u 0u v u (b) (i) 0 m/s (ii) m ) (a) (b) (i) u u sin sin sin ) (a) (i) 0 N (ii) 6 N cos cos ) (b) (i) u u e e 6) (a) 9) (a) (i) cm (ii) 008 k 0) (a) h ) (a) 80 N (b) tan y e (b) (ii) 6 m/s (iii) 9 J 00 ) (a) (ii) m 6 m (b) (i) m/s (ii) 6 ) (a) (i) E of N (ii) 86 s (b) (i) 806 m/s 88 S of E (ii) m (iii) 6 s v ) (a) 0 m ) (a) (i) m/s (ii) (b) (ii) m/s (iii) 0 m u u ) (a) (i) e e (ii) e (b) (i) 60 (ii) 8 8 6) (a) 8 r (b) (ii) 6 8 W ) (a) ½ l (b) (i) (ii) 08W 8) (b) (i) 08 J (ii) 06 m 9) (a) 8 cm (b) (i) (ii) W 0) (a) ye (b) (ii) 00 ) (a) (ii) m (b) (i) m/s ) (a) v 0i 0 j km/h (b) (i) 90 m/s 9 S of E (ii) 88 m m ) (a) 8 (b) ) (a) (i) e e W u sin sin ) (a) cos m/s (b) (ii) 6 m u u (ii) 0 e (b) (ii) ½ 6) (a) (i) cm (ii) cm/s (b) (ii) 66 6 6 ) (a) (iii) 8) (b) (i) l (ii) l 9) (a) (iii) 0 0 N (b) cm y (b) (ii) 6 s 0) (a) Dominick Donnelly wwwappliedmathematicsie 0 Pae
00 ) (a) (i) 8 m/s (ii) 0 m/s ) (a) (i) 8660 m (ii) 960 s (b) 6 km/hr 6 N of E ) (a) (ii) ) (a) cm (b) (i) (ii) N ) (a) 08 8) (b) (ii) 960 J 9) (a) 8 (b) 8 0) (a) yln( e ) (b) (i) ln s or s (ii) 66 m (iii) 00 m/s 00 ) (a) s 60 s ) (b) 88 km ) (a) m/s (b) h ) (ii) m/s m/s m/s m/s (iii) u u m ) (a) (i) 9 e 9 e e 6) (a) (i) 8) (b) l l A cm T (ii) cm/s (b) (i) (ii) ) (b) W 8sin 8 mr ma 9) (a) 000 m 0000 m r r d y dy y y ln d d 0) (a) 000 ) (a) 6 m/s (b) (i) s 8 m m (ii) q 0 s ) 0 a a a (i) a (ii) u ) (a) (b) 66 or ) (a) 9 m (b) (iii) m/s 6) (a) k 0 k 0 06 rad/s (b) (i) (ii) 0 (iii) k k k l W ) (a) (ii) (b) (ii) 6cos cos 8) (b) (i) m/s (ii) 9 s 9) (a) 0 cm 0) (a) (b) (i) (ii) e e e 999 ) (a) (i) N (ii) 880 W (b) /t (ii) 6 m ) (a) 08 m/s (b) (i) S of W (ii) 8 km ) (a) (i) tan or (b) (i) ) (a) (i) /8 (ii) 0 and 0 (b) (iii) 0/ ) (a) (ii) Both collisions occur at the same spot (b) m/s 6) (a) 9 tan 9 66sin t or 66 cos t 0 (b) (i) 08 m from p (ii) a 0 ) (b) tan - 6 8) (b) (i) 08 m (ii) 08 (iii) 0 m from centre ln 9) (a) (b) 0008 k 0) (a) v tan (b) i 86 m/s (ii) % 998 ) (a) (b) (i) u = 0 b = (ii) 9 m ) (a) (i) 9 N of W (ii) 6 s (b) (i) 9 or 86 N of E (ii) s or s ) (a) (i) tan - or (b) (i) (ii) ) (a) (i) m/s (ii) 9 N (b) m m ) (a) (ii) e (b) m 6) (a) (ii) (b) (ii) 0 m 8) (c) (ii) 8l 9) (a) (i) 08 N (ii) 0) (a) 8 v e Dominick Donnelly wwwappliedmathematicsie 0 Pae
99 ) (a) (i) 6 (ii) m ) (ii) 08i j ) (a) (i) m ) (a) (i) 0 (ii) (ii) m = (b) (i) T km kma m T m a ) (a) (i) u (b) (i) ) (a) (i) T W (ii) k 0 00 tan (iii) T m (b) (ii) m u u u m e i j e i 0 j (ii) e 6) (i) T (iii) 0 sin 6 0) (a) 08 (b) (i) 0 m/s (ii) 8 s W (b) (i) T W (ii) cm 9) (a) 6 m (b) (i) k (ii) 0 996 ) (a) (i) m/s (ii) oa m ) (i) 9 S of E (ii) km/hr (iii) km (iv) 0 hr 8 6 ) (ii) k: k: k: (iii) m 6) (a) (i) 08 (ii) 09 m (iii) 6 m/s ) (a) W 9 9 9 9 8) (b) (i) 6r p r (ii) 6 r 9) (b) and 0) (a) y e sin 99 ) (a) (i) u (b) (i) 6 (ii) (iii) 8 m ) (a) (i) 6 6t 6 8t (ii) 6 (b) (i) p = 06 q = 0 (ii) s ) (a) (i) m and 9 m (ii) 06 m (iii) 6 m/s (b) (i) 09 (ii) tanβ < 0 β is obtuse ) (i) (ii) (iii) (iv) v u e v u e (ii) 9 9 9) (a) 0 litres (b) (i) (ii) 0098 N (iii) 8 cm 0) (a) y 8tan 99 ) (a) 6 m (b) (i) 9 (ii) ) (a) (i) ij 98 m/s f qt j (ii) 0 (ii) m m (b) (i) 0t i ) (a) (i) 0 (ii) 0 m (b) (i) m/s (ii) 6 m/s ) (ii) m (iii) r 6) (i) 6 m/s (ii) 668 N (iii) m ) (i) W Wtan 8) (i) 9 9) (a) (i) 9 m (ii) 08 N 0) (a) y (b) (ii) 6 s e 99 ) (a) (i) a m/s u m/s (b) (i) s (ii) 096 m ) (a) 6 m/s SW (b) (i) straiht across (ii) 90 s (iii) m ) (b) (i) u t u t v i j r ut t i ut t mu j (ii) 60 ) 0 6) (a) (i) 6 l (ii) 09 m/s (b) (ii) 8) (b) (ii) s 9) (a) cm (b) (ii) l 0) (a) y 8 (b) (ii) 0 m Dominick Donnelly wwwappliedmathematicsie 0 Pae
99 ) (a) 6 m (b) (i) after s and s (ii) m ) (i) 9 E of N (ii) 6 hours (iii) 6 hours 0 ) (i) tan tan ) (ii) u u i j i j (iii) 6 6 6) (a) (ii) (b) (ii) s (iii) W tan r s ) (b) (ii) 8) (b) tan 9) (a) 00 m (b) (i) 066 (ii)00 0) (a) (b) (i) ln9 (ii) 0 ln 99 ) (a) (i) 600 m (ii) 0 s (b) ) (i) m E m E (ii) u 96 ) (ii) 0u 6 S of W ) (i) 0u 96 e i j e i j (ii) 6) (a) ) (b) (i) u (ii) (b) ) (i) W tan 8) (b) (i) 88 s (ii) 088 m 9) (ii) 9 6 0) (a) y 990 ) (b) (ii) t s ) (a) 8 i8 j m/s (b) (i) 6 s (ii) 69 s 6) (b) 9: pm ) (b) 8) (b) (i) a (ii) m 9) (a) 0 cm (b) (i) cm (ii) 60 N/m 0) (a) y 989 ) (ii) 8 m ) (i) m/s from 60 S of W (ii) 09 S of W ) (ii) or (iii) 80 ) (i) tan (ii) 6) (ii) 069 s (iii) 06 m/s ) (i) 69 (iii) N r 8) 9) (a) m (b) T 00 N R 088 N 0) (a) y 988 e ) (a) m/s (b) m ) (b) 800 s u ) (a) 8 or 6 9 ) (ii) m/s m/s m/s N ) (i) 0 0 0 0 (ii) u 9u (iii) 98 6) (i) v (iii) 0 m ) (iii) W horizontally 8) l l s 9) (i) 0) (a) sin t (b) 8 s 98 ) (a) 0 s ) (i) 88 km/hr 86 N of W (ii) hr hrs & 9 mins ) (ii) m/s d ) (i) v A i j vb i p j (iii) 6) (ii) s ) (iii) 8 N 8) (i) p s 9) (a) (i) 0 k (ii) k (b) (ii) 0) (a) y (b) 6 s 986 ) (a) (ii) s (b) s ) (i) 6 m (ii) 69 m ) s ) (ii) ) (a) (i) 6) (a) s 089 m 9) (a) d (b) 08 0) (a) y e Dominick Donnelly wwwappliedmathematicsie 0 Pae 6
98 ) (i) u v u v (ii) u v ) (i) t t v u cos i usin j t t ) (i) r u cost i usint u sin u sin j (ii) (iii) ) (ii) (iii) 8 ) (iii) 6 ) (a) s (b) (i) 600 W (ii) 96 m/s 6) (i) 0π m/s (ii) 08 s (iii) (iv) 8) (ii) (iii) 9) (a) (i) 9 (ii) k 6k (iii) (b) 6 m 0) (a) y (b) (ii) 98 ) (a) 06 m/s (b) (i) 6 s (ii) 8 m ) (i) 0 m/s at 9 N of W (ii) 9 m (iii) 0 s u sin ) t ) (a) N 98 u R ) (ii) ) (b) 6) (a) (b) (ii) (b) : 9) (a) (i) 6 (ii) 09 (iii) ml (b) d kt c 0) (a) v e k (b) u ln ) s m/s d v ) ) (i) m/s (ii) N N ) s 0 m v 6 ) (i) i j m/s (ii) i j m/s ; 6) (iii) ) (i) m m (ii) m m 8) m 06 m 00 s 9) (a) 806 k/m 0 mm (b) (i) r (ii) r 0) (a) y sin (b) 00 m/s 00 m Dominick Donnelly wwwappliedmathematicsie 0 Pae