Question

What are the magnitude Δ and angle of the change in velocity if the initial velocity is 65.0 m/s south and the final velocity is 20.0 m/s west? Let the angle be measured relative to the east direction (e.g., =90∘ means Δ⃗ points north, =180∘ means Δ⃗ points west, etc.).

Answer 1

• ∆ = 68.0
• ∠ = 107.1°

Step-by-step explanation:

You want the magnitude and direction of the change in velocity from 65.0 m/s south to 20.0 m/s west.

Change

The change in velocity can be represented by a vector from the initial velocity to the final velocity as shown in the attachment. The magnitude and direction of it can be found using the usual tools for solving triangles.

Magnitude

The magnitude of the change is the hypotenuse of a right triangle with legs 20 and 65. Its value is ...

∆ = √(20² +65²) = √4625 ≈ 68.007 . . . . m/s

The magnitude of the velocity change is ∆ = 68.0 m/s.

Direction

As the diagram shows, the direction of the change is west of north by an angle θ that satisfies ...

tan(θ) = 20/65

θ = arctan(20/65) ≈ 17.1027°

The direction of the change measured from east is 90° +17.1° = 107.1°.

The angle of the velocity change is about 107.1°.

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Additional comment

These calculations are handled neatly by a vector calculator, as shown in the second attachment.