An airplane pilot wishes to fly due west.a wind of80.0km/hris blowing toward the south .
a)if the speed of the plane (it's speed in still air)is 320.0km/hr ,in which direction should the pilot head? And what is the speed of the plane over the ground .illustrate with a vector diagram.
Well, he will fly N of W at an angle of arcsin(80/320). (sketch this out so you can see why)
speed over ground: sqrt(320^2-89^2)=about 307km/hr.
To determine the direction in which the pilot should head and the speed of the plane over the ground, we will combine the velocities of the wind and the plane using vector addition.
Step 1: Draw a diagram:
Start by drawing a coordinate system with a north-south (vertical) axis and an east-west (horizontal) axis. Label the north direction as positive and the west direction as negative.
Step 2: Calculate the wind vector:
The wind vector is given as 80.0 km/hr towards the south. Since the pilot wants to fly due west, we have to take the opposite direction of the wind. So the wind vector will be -80.0 km/hr in the south direction.
Step 3: Calculate the plane's velocity vector:
The speed of the plane (velocity in still air) is given as 320.0 km/hr. Since the plane wants to fly due west, the velocity vector of the plane will be -320.0 km/hr in the west direction.
Step 4: Add the vectors:
To find the resultant velocity vector, add the wind vector and the plane's velocity vector together. In this case, we are adding a vector to the left (west) and a vector downwards (south). Start by placing the tail of the second vector at the head of the first vector. The resulting vector is the vector that connects the tail of the first vector to the head of the second vector.
Step 5: Find the direction:
Measure the angle between the resultant vector and the west direction line using a protractor. This angle represents the direction the pilot should head.
Step 6: Find the speed over the ground:
Measure the length of the resultant vector using a ruler. This length represents the speed of the plane over the ground.
By following these steps, you will be able to determine in which direction the pilot should head and the speed of the plane over the ground.