An aeroplane is heading 20 degree North of East,flying at 200km/hr relative to the air. Simultaneously the wind carriers the plane 10degree East of South at speed of 60.0km/hr.
(a) find the velocity of the relative to the ground.(you may solve it graphically)
(b) find the components (East and North) of the velocity of the plane relative to the air and of the relative to the ground. Find the plane's velocity relative to the ground by adding comments.
(a) use the law of cosines:
v^2 = 200^2 + 60^2 - 2*100*60*cos(80°)
v = 198.6 km/hr at 2.7° N of E
Now use that to break it into components.
To solve this problem, we can break down the problem into two components: the plane's velocity relative to the air, and the wind's velocity relative to the ground. We can then combine these two components to find the plane's velocity relative to the ground.
(a) Finding the velocity of the plane relative to the ground:
1. Draw a diagram to visualize the problem:
- Draw a vector representing the plane's velocity relative to the air (20 degrees north of east, 200 km/hr).
- Draw a vector representing the wind's velocity relative to the ground (10 degrees east of south, 60 km/hr).
2. Find the components of the plane's velocity relative to the ground:
- Since the plane's velocity relative to the air is 20 degrees north of east, we can break it down into east and north components using trigonometry.
East component = 200 km/hr * cos 20°
North component = 200 km/hr * sin 20°
3. Find the components of the wind's velocity relative to the ground:
- Since the wind's velocity is 10 degrees east of south, we can break it down into east and north components using trigonometry.
East component = 60 km/hr * sin 10°
North component = -60 km/hr * cos 10° (negative because it's heading south)
4. Add the east and north components of the plane's velocity relative to the ground:
East component = plane's east component + wind's east component
North component = plane's north component + wind's north component
5. Calculate the magnitude and direction of the plane's velocity relative to the ground:
Magnitude = sqrt((East component)^2 + (North component)^2)
Direction = arctan(North component / East component)
(b) Finding the components of the velocity of the plane relative to the air and relative to the ground:
1. The components of the plane's velocity relative to the air are already calculated:
East component = 200 km/hr * cos 20°
North component = 200 km/hr * sin 20°
2. The components of the plane's velocity relative to the ground are already calculated:
East component = plane's east component + wind's east component
North component = plane's north component + wind's north component
3. Adding comments to find the plane's velocity relative to the ground:
Plane's Velocity relative to the ground = (East component relative to ground, North component relative to ground)