A man travelled 7km due north then 10km due east.find the resultant displacement
From your sketch you should see that
distance^2 = 7^2 + 10^2 = 149
distance = √149 = appr 12.2
Find resultant displacement
To find the resultant displacement, we can use the concept of vectors.
Step 1: Represent the two displacements as vectors.
- The displacement of 7 km due north can be represented as a vector v1 with magnitude 7 km and direction pointing upwards.
- The displacement of 10 km due east can be represented as a vector v2 with magnitude 10 km and direction pointing towards the right.
Step 2: Add the two vectors to find the resultant displacement.
- To add the vectors, we can use vector addition. Place the tail of vector v1 at the origin (0,0) and draw vector v1 upwards on the y-axis. Then, place the tail of vector v2 at the head of vector v1 and draw vector v2 towards the right along the x-axis.
- The resultant displacement is the vector that connects the initial point (tail of v1) to the final point (head of v2). Draw this vector.
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant displacement.
- The magnitude of the resultant displacement can be found using the Pythagorean theorem: magnitude = √(x^2 + y^2), where x and y are the horizontal and vertical components of the resultant displacement.
- In this case, the horizontal component is 10 km and the vertical component is 7 km. Calculate the magnitude using: magnitude = √(10^2 + 7^2) = √(100 + 49) = √149 ≈ 12.2 km.
Step 4: Determine the direction of the resultant displacement.
- To find the direction, we can use trigonometry. The angle between the resultant displacement and the positive x-axis can be found using: θ = tan^-1(y/x), where x and y are the horizontal and vertical components of the resultant displacement.
- In this case, y = 7 km and x = 10 km. Calculate the angle using: θ = tan^-1(7/10) ≈ 35.5 degrees.
Therefore, the resultant displacement is approximately 12.2 km in magnitude, and it is at an angle of approximately 35.5 degrees with the positive x-axis.