A bird moves with velocity 20 m/s in a direction making an angle of 60° with the eastern line and 60° with vertical upward. Represent the velocity vector in rectangular form.

To represent the velocity vector of the bird in rectangular form, we need to break it down into its components along the x (east-west) and y (up-down) axes. Given that the velocity is 20 m/s at an angle of 60° with the eastern line and also 60° with the vertical, we can use trigonometric functions to find these components.

Calculating Components

We can use the following formulas:

• Vx (horizontal component) = V * cos(θ)
• Vy (vertical component) = V * sin(θ)

Step 1: Determine the Angles

Since the bird's angle with the vertical is also 60°, we can deduce that:

• The angle with the horizontal (eastern line) is 30° (90° - 60°).

Step 2: Calculate the Components

Now, we can calculate the components using the velocity of 20 m/s:

• Vx = 20 m/s * cos(30°) = 20 * (√3/2) ≈ 17.32 m/s
• Vy = 20 m/s * sin(30°) = 20 * (1/2) = 10 m/s

Final Velocity Vector

The rectangular form of the velocity vector can be expressed as:

V = (17.32 i + 10 j) m/s

Here, i represents the eastward direction, and j represents the upward direction. Thus, the bird's velocity vector in rectangular form is approximately 17.32 m/s east and 10 m/s upward.