an aeroplane flies horizontally at 80m/s in still air if the aviator wishes to fly due south and the wind is blowing from the south-east at 30m/s

Question

an aeroplane flies horizontally at 80m/s in still air if the aviator wishes to fly due south and the wind is blowing from the 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

Answer 1

If you want an expert to see your post, please put the name of the school subject in the appropriate box.

Answer 2

I have little or no answer.

I want answers to the question.
Any help? ???

Answer 3

To answer these questions, we need to consider the vector addition of the plane's velocity and the wind's velocity. We can first find the resultant velocity (ground speed) and then calculate the required course and time.

1. Finding the resultant velocity (ground speed):
To find the resultant velocity, we need to add the velocities of the plane and the wind as vectors. We will break down the velocities into their horizontal (east-west) and vertical (north-south) components.

Given:
Plane velocity in still air (Vplane) = 80 m/s (horizontally)
Wind velocity (Vwind) = 30 m/s (south-east)

We can calculate the horizontal and vertical components of the wind velocity:
Horizontal component of Vwind = Vwind * cos(45°) [since it is 45° south-east]
= 30 m/s * cos(45°)
= 30 m/s * 0.7071
= 21.21 m/s (eastward)

Vertical component of Vwind = Vwind * sin(45°) [since it is 45° south-east]
= 30 m/s * sin(45°)
= 30 m/s * 0.7071
= 21.21 m/s (southward)

Now, we add the horizontal components of the plane and wind velocities:
Horizontal component of resultant velocity = Vplane + Horizontal component of Vwind
= 80 m/s + 21.21 m/s
= 101.21 m/s (eastward)

And we add the vertical components of the plane and wind velocities:
Vertical component of resultant velocity = 0 (since the plane flies horizontally)

Therefore, the resultant velocity (ground speed) is:
Vresultant = √[(Horizontal component)^2 + (Vertical component)^2]
= √[(101.21 m/s)^2 + (0 m/s)^2]
= √(10,243.44 m^2/s^2)
≈ 101.21 m/s (eastward)

So, the plane will have to steer a course in the eastward direction.

2. Finding the time taken to reach the destination:
To find the time taken, we can use the formula: time = distance / speed

Given:
Distance = 200 km = 200,000 m
Ground speed (Vresultant) = 101.21 m/s

Time taken = Distance / Ground speed
= 200,000 m / 101.21 m/s
≈ 1,975 seconds
≈ 33 minutes (approximately)

Therefore, it will take approximately 33 minutes for the plane to reach its destination, flying at a ground speed of 101.21 m/s.

an aeroplane flies horizontally at 80m/s in still air if the aviator wishes to fly due south and the wind is blowing from the south-east at 30m/s

If you want an expert to see your post, please put the name of the school subject in the appropriate box.

I have little or no answer.

15.4°

To answer these questions, we need to consider the vector addition of the plane's velocity and the wind's velocity. We can first find the resultant velocity (ground speed) and then calculate the required course and time.