The diagram shows a river,500m wide between the straight parallel banks where AD = 500m and DB = 2000. A man swims across the river from A to C at 0.5 m/s and then he runs along the banks from C to B at 0.8 m/s
(a)If he swims in the direction AC making an angle of Ɵ and reaches C in t seconds, show that t = 1000cosec Ɵ
(b)If T(in seconds) is the total time taken from A to B, express T in terms of Ɵ
(c)Find the minimum value of T in minutes and seconds, correct to the nearest second.
(a)
Using trigo ratio,
sin Ɵ = 500/AC
AC = 500/sin Ɵ
= 500cosec Ɵ
0.5 = 500cosec Ɵ/t
T = 1000cosec Ɵ
(b)
BC = 2000 – DC
BC = 2000 – 500/tan Ɵ
TBC = BC/s = 2500 – 625/tan Ɵ
Total time, T = tAC + tBC
= 1000cosec Ɵ + 2500 – 625/tan Ɵ
(c)
