To calculate the relative velocity of car A with respect to car B, we need to find the velocity vector of car A with respect to an observer moving with car B.
Let's assume that car B is at rest and the observer is moving with it. This means that the velocity of car B with respect to the observer is zero, and the velocity of the observer is the same as that of car B.
Now, let's calculate the velocity of car A with respect to the observer:
Velocity of car A = 120 km/h north-east
Velocity of observer = 140 km/h west
To find the velocity of car A with respect to the observer, we subtract the velocity of the observer from the velocity of car A:
Velocity of car A with respect to observer = Velocity of car A - Velocity of observer
= (120 km/h north-east) - (140 km/h west)
As north-east is at an angle of 45 degrees from north, and west is 270 degrees from north, we can write this as:
= 120(cos(45)i + sin(45)j) - 140(cos(270)i + sin(270)j)
= 120(0.707i + 0.707j) - 140(-1i)
= 84.84i + 84.84j - 140i
= -55.16i + 84.84j
The magnitude of the velocity of car A with respect to the observer is then calculated as follows:
|Velocity of car A with respect to observer| = sqrt((-55.16)^2 + (84.84)^2)
= sqrt(3050.83 + 7183.86)
= sqrt(10234.69)
= 101.16 km/h
Therefore, the magnitude of the velocity of car A relative to car B is 101.16 km/h, with the direction being approximately 56.31 degrees north of east.
Two cars simultaneously pass a fork in a road. Car A travels north-east at 120 km/h and car B travels west at 140 km/h. Calculate the velocity of car A relative to car B in magnitude and direction
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