F.5 MATHS

(a) After 10s, OA=400 m, OB=300 m. Using cosine formula

AB=√[OA^2+OB^2-2(OA)(OB)cos120]

After Sub. the values, we can find that AB=608.2763 m

(b) Generally, after t seconds OA=40t m, OB=30t m
So AB
=√[OA^2+OB^2-2(OA)(OB)cos120]
=√[1600t^2+900t^2-2(40t)(30t)cos120]
=√3700t^2
=√3700t

dAB/dt=√3700 m/s which is the rate of change of distance between the cars with respect to time.

a.)
Distance between two cars
= [400^2 + 300^2 - 2(400)(300)cos120deg]^(1/2)
= 608.3 m (corr to 1 d.p.)

b.)Rate of change
= 608.3m / 10s
= 60.83m/s