velocity

Question

1.2 A cyclist is cycling at 8 m/s to his destination due north. There is a wind blowing at 3 m/s from the south-east. Calculate the resultant velocity of the cyclist in magnitude and direction.

Answer 1

Cycling speed = 8 m/s

Cycling direction = north

Wind blowing speed =  3 m/s

Wind direction = south-east

The picture representation of problem is

Consider

a = OA = CB = 8 m/s

b = OB = AC = 3 m/s

c = OC = relative speed

Angle C = ∠AOC = ∠AOE + ∠BOE

Angle C = 90 + 45 = 135^o

So the relative velocity can be calculated using cosine rule.

c² = 8² + 3² -2(8)(3) cos(45°) 

c² = 64 +9 - 47.81

c² = 30.05

c = 6.25 m/s

The relative velocity  is 6.25 m/s .

The direction of two cars can be calculated using formula : .

cos(∠AOC)	=	b2 + c2 – a2
		2bc

cos(∠AOC)	=	6.252 + 82 – 32
		2 × 6.25 × 8

cos(∠AOC)	=	94.0625
		100

cos(∠AOC) = 0.94

∠AOC = 19.8^o

the resultant velocity of the cyclist in direction is 19.8° right side to north side.