What are the magnitude δv and angle θ of the change in velocity if the initial velocity is 30.0 m/s south and the final velocity is 75.0 m/s west? let the angle θ be measured relative to the east direction (e. g., θ=90∘ means δv⃗ points north, θ=180∘ means δv⃗ points west,

Magnitude of δv = 80.78 m/s

Angle , θ =

Explanation:

   Here east direction is zero degree, that is zero degree is along positive X direction, north is along + Y direction, West is along - X direction and South is along -Y direction.

    In this case initial velocity = 30.0 m/s south = -30 j

                         Final velocity = 75.0 m/s west  = - 75 i

    We know that change in velocity =  Initial velocity - Final velocity

                                       So            δv = - 75 i - (-30 j)

                                                             =  - 75 i + 30 j m/s

   Magnitude of δv =

   Angle , θ =

The magnitude of the velocity is 80.78m/s

Since tan is negative in the third quadrant, hence

If the initial velocity moves towards the south, the velocity will be 30.0m/s j

If the final velocity is 75.0 m/s west, hence the direction will be -75m/s i

The magnitude of the velocity will be expressed as;

Hence the magnitude of the velocity is 80.78m/s

Get the angle between the velocities

Since tan is negative in the third quadrant, hence

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