calculate velocity

Question

1.1 Two cars leave a fork in a road simultaneously. Car V travels at 60 km/h to the west and car W travels at 100 km/h in a direction N 45° E. Calculate the relative velocity of car W with respect to car V in magnitude and direction.

Answer 1

Car V travels at 60 km/hr to west .

car W travels at 100 km/h in a direction NE .

So the relative velocity  can be determined by the below diagram .

 

So the relative velocity can be calculated using cosine rule .

c² = 60² + 100² -2(60)(100) cos(135°) 

c² = 3600 +10000 + 8485.28

c² = 22085.28

c = 148.611

The relative velocity  is 148.611 km/hr .

 The direction of two cars can be calculated using sine rule .

sin A / 60  = sin 135 / 148.611

sin A =  0.000475 * 60

sin A = 0.2854

A = arcsin ( 0.2854)

A = 16.58°

 The direction of aircraft with respect to OR Tambo International Airport is 16.58° .