a plane flies at 430mph the bearing from Paris to Moscow is 78drgrees and the distance is 1800 mi if the wind is blowing 65mph at 340degrees what heading will take you from Paris to Moscow and how long will it take? include drawing and trip back
This is a math problem help i need the answer and to show my work.Mr.Pham mowed 2/7 of a lawn.His son mowed 1/4 of it.Who mowed the most?How much if the lawn still needs to be mowed?
13/28
To determine the heading that will take you from Paris to Moscow, and how long it will take, we can use vector addition and trigonometry.
First, we'll draw a diagram to visualize the situation. Let's assume that east is the reference direction, and the angle increases counterclockwise.
1. Draw a line segment representing the direction from Paris to Moscow, with a length of 1800 miles.
2. Label one end of the line segment as "Paris" and the other end as "Moscow."
3. Draw an arrow from Paris to Moscow representing the airplane's heading at a bearing of 78 degrees.
4. Draw another arrow from Paris to Moscow representing the wind's direction at a bearing of 340 degrees.
Now, let's break down the velocities:
1. The velocity due to the plane's heading can be represented by a vector with a magnitude of 430 mph. This vector will be in the direction of the bearing (78 degrees), so draw an arrow with a length of 430 units and align it with the line segment from Paris to Moscow.
2. The velocity due to the wind can be represented by a vector with a magnitude of 65 mph. Since we know the bearing of the wind (340 degrees) relative to east, we can subtract this angle from 180 degrees (which gives us the angle relative to the bearing from Paris to Moscow). Drawing an arrow with a length of 65 units in this direction will represent the wind's effect.
Now, to calculate the resultant velocity and the time it takes to travel from Paris to Moscow:
1. Use vector addition to find the resultant velocity by adding the velocity vector of the plane to the velocity vector of the wind. Draw an arrow starting from the tail of the plane's velocity vector and ending at the tip of the wind's velocity vector. This represents the resultant velocity.
2. Measure the magnitude (length) of the resultant velocity arrow. This will give you the speed of the airplane relative to the ground.
3. To find the heading (angle) of the resultant velocity, measure the angle between the line segment from Paris to Moscow and the resultant velocity arrow. This will be the heading you need to follow.
4. To calculate the time it takes, divide the distance from Paris to Moscow (1800 miles) by the magnitude of the resultant velocity.
To find the heading and time for the trip back, reverse the process:
1. Use vector addition again, but this time subtract the wind's velocity vector from the plane's velocity vector.
2. Measure the magnitude and heading of the resultant velocity to determine the heading and time for the trip from Moscow back to Paris.
By following these steps, you can determine the heading and time for both the trip from Paris to Moscow and the trip back from Moscow to Paris.