Solve the given problem and show your solution using separate sheets of paper.
1. Draw the vectors of the following displacements:
a. The horizontal displacement of a car is 30 km west.
b. An airplane’s displacement is equal to 80 km, 70o east of north.
2. A motorcycle is driven 50 km west, then 30 km south, and 25 km, 30o west of south. Show the vector diagram and find the total displacement of the motorcycle from its starting point.
To solve these problems and show the solution using separate sheets of paper, follow these steps:
1. Draw a coordinate axes system on each sheet of paper to represent the directions of displacement. Label the x-axis as east-west and the y-axis as north-south.
For Problem 1a:
- On the first sheet of paper, mark a starting point (origin) with a small dot.
- Move 30 km to the left (west) from the origin along the x-axis.
- At the end point, draw an arrow pointing to the left to represent the 30 km westward displacement of the car.
For Problem 1b:
- On the second sheet of paper, again mark a starting point (origin) with a small dot.
- From the origin, move 80 km in the direction 70 degrees east of north. To do this, draw a line at a 70-degree angle from the positive y-axis.
- Measure 80 units along this line and mark the end point.
- Draw an arrow from the origin to the end point to represent the airplane's displacement. Make sure the arrow points in the direction of the displacement.
2. For Problem 2:
- On a new sheet of paper, draw a coordinate axes system as before.
- Mark a starting point (origin) with a small dot.
- First, move 50 km to the left (west) from the origin along the x-axis.
- From this new point, move 30 km downwards (south) along the y-axis.
- To incorporate the 25 km, 30 degrees west of south, we need to consider it as an additional displacement from the second point.
- Draw a line at a 30-degree angle towards the west from the south.
- Measure 25 units along this line and mark the end point.
- Draw an arrow from the second point to the new end point to represent the additional displacement.
- Finally, draw a line connecting the starting point to the new end point, which represents the total displacement of the motorcycle.
- Measure the length of this line using a ruler or scale, and note the value.
By following these steps and drawing the vectors of displacement on separate sheets of paper, you will find the solution to the given problems and have a visual representation of the solution.