a bird is flying through the air with an air speed 12.6m/s heading 27.7 west of north. it is a windy day with wind velocity blowing at 8.95m/s heading 12.5 south of west. what is the velocity of the bird as seen by a person on the ground
To find the velocity of the bird as seen by a person on the ground, we need to add the vectors of the bird's airspeed and the wind velocity.
First, let's break down the airspeed of the bird into its northward and westward components:
- The northward component of the bird's airspeed can be found using the formula: v_north = airspeed * sin(angle)
v_north = 12.6 m/s * sin(27.7°)
v_north ≈ 5.91 m/s
- The westward component of the bird's airspeed can be found using the formula: v_west = airspeed * cos(angle)
v_west = 12.6 m/s * cos(27.7°)
v_west ≈ 10.99 m/s
Next, let's break down the wind velocity into its northward and westward components:
- The northward component of the wind velocity can be found using the formula: v_north = wind velocity * sin(angle)
v_north = 8.95 m/s * sin(12.5°)
v_north ≈ 1.85 m/s
- The westward component of the wind velocity can be found using the formula: v_west = wind velocity * cos(angle)
v_west = 8.95 m/s * cos(12.5°)
v_west ≈ 8.73 m/s
Now, we can find the total northward and westward velocity of the bird:
- The northward velocity is the sum of the bird's airspeed northward component and the wind velocity northward component:
total northward velocity = v_north (bird airspeed) + v_north (wind velocity)
total northward velocity ≈ 5.91 m/s + 1.85 m/s ≈ 7.76 m/s
- The westward velocity is the sum of the bird's airspeed westward component and the wind velocity westward component:
total westward velocity = v_west (bird airspeed) + v_west (wind velocity)
total westward velocity ≈ 10.99 m/s + 8.73 m/s ≈ 19.72 m/s
Therefore, the velocity of the bird as seen by a person on the ground is approximately 7.76 m/s directed northward and 19.72 m/s directed westward.