A motor car is going due north at a speed of 50km/h.It makes a 90 left turn without changing the speed. The change in the velocity of the vehicle is A. 50 km/h towards westB. 70 km/h towards south-westC. 70 km/h towards north-westD. Zero

The change in velocity of the vehicle can be calculated using vector addition since both the initial velocity (50 km/h north) and the change in velocity (due to the left turn) are vectors.

When the car makes a 90-degree left turn, it changes its direction but not its speed. This change in direction can be represented as a vector pointing to the left (west) with a magnitude equal to its initial velocity of 50 km/h.

Now, we have two velocity vectors to add:

The initial velocity (50 km/h north) can be represented as 50 km/h in the +Y direction.
The change in velocity due to the left turn (50 km/h west) can be represented as 50 km/h in the -X direction.
To find the resultant velocity, we can use the Pythagorean theorem to calculate the magnitude (speed) of the resultant vector:

Resultant speed = √[(50 km/h)^2 + (50 km/h)^2] = √[2500 km^2/h^2 + 2500 km^2/h^2] = √(5000 km^2/h^2) = 50√2 km/h ≈ 70.71 km/h (rounded to two decimal places)

Now, to find the direction of the resultant velocity, we can use trigonometry. The angle θ between the initial velocity (north) and the resultant velocity can be found using the inverse tangent (arctan):

θ = arctan(50 km/h / 50 km/h) = arctan(1) = 45 degrees

So, the resultant velocity is 70.71 km/h at an angle of 45 degrees counterclockwise from the initial velocity. Since 45 degrees counterclockwise from north is northwest, the answer is:

C. 70 km/h towards north-west.