An aeroplane flies horizontally at 80m/s in still air. If the aviator wishes to fly due south and the wind is blowing from south-east at 30m/s.(1) what course must he steer?(2)how long will it take him to arrive at his destination 200km away?
What direction is the plane flying? It makes a difference in the final velocity.
Actually, I was wrong. You want two vectors
v + w = <0,-y>
where y is the final speed of the plane.
If v is the velocity of the plane, then v = <x,√(80^2-x^2)>
and w is the wind's velocity, which is <21.2,-21.2>
So now, add up the x- and y-components and solve for the values to use.
1. Vp + Vw = -80i
Vp + 30[135o] = -80i,
Vp -21.2 + 21.2i = -80i,
Vp = 21.2 - 101.2i = 103.4m/s[-78.2o].
Direction = 78.2 degrees S. of E. = 11.8o E. of S.
2. V*T = 200,000 m.
80T = 200,000 ,
T = 2500 s. = 41.7 min.
To answer these questions, we need to break down the given information and apply vector addition principles to determine the course and time of travel.
1. To determine the course the aviator must steer, we need to find the resultant velocity by adding the velocity of the airplane in still air to the velocity of the wind.
Let's define the vectors:
- Velocity of the airplane in still air (A) = 80 m/s (due south)
- Velocity of the wind (W) = 30 m/s (blowing from southeast)
To find the resultant velocity (R), we add these vectors:
R = A + W
To visualize this, draw a scale diagram where the airplane velocity points directly downward (due south) and the wind velocity is directed from the southeast. Using vector addition rules, draw the resultant vector, which will represent the resultant velocity.
Once the resultant vector is drawn, measure its angle with respect to the south direction (usually clockwise). This angle represents the course the aviator must steer.
2. To determine the time it takes to travel 200 km, we can use the equation:
Time = Distance / Speed
First, let's convert the given distance of 200 km into meters:
200 km = 200000 meters
To find the speed, we need to consider the resultant velocity obtained from the previous step.
Speed = Resultant velocity magnitude = ||R||
Now we can substitute the values into the equation to find the time:
Time = 200000 meters / Speed
Calculating the final result will depend on the specific values obtained for the resultant velocity and can be easily done using a calculator.
Remember to consider kinematic approximations and neglect any other external factors that might affect the flight path, such as air resistance or changes in wind speed at different altitudes.