A bird flying west at 35m/s dives south at 35m/s. Did the bird’s velocity change, if so how?
Yes, the bird's velocity changed when it dived south.
Velocity is a vector quantity that includes both speed and direction. In this case, the bird initially was flying west at a speed of 35 m/s. However, when it dived south, its direction changed. The combination of speed and the change in direction means that the velocity of the bird has changed.
To calculate the final velocity, you can use vector addition. In this case, the bird's initial velocity can be represented as 35 m/s towards the west, and the dive can be represented as 35 m/s towards the south.
To add these velocities vectorially, you can use the Pythagorean theorem to find the magnitude of the resultant velocity and trigonometry to find its direction.
By using the Pythagorean theorem, you can calculate the magnitude of the resultant velocity:
Resultant speed = √(35^2 + 35^2) = √(1225 + 1225) = √(2450) ≈ 49.49 m/s
To find the resultant direction, you can use trigonometry.
tanθ = opposite/adjacent = 35 m/s / 35 m/s = 1
θ = tan^(-1)(1)
θ ≈ 45°
Therefore, the bird's final velocity is approximately 49.49 m/s at a direction of 45° south of west.