A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find x
To find the angle x, we can use the concept of vectors and the angle between them.
Step 1: Determine the velocity vectors of Car A and Car B.
- Car A is going north-east, which can be represented by a vector pointing in that direction.
- Car B is going south-east, which can be represented by a vector pointing in that direction.
Step 2: Calculate the resultant velocity vector, which represents the relative velocity of Car A with respect to Car B.
- To calculate the resultant velocity vector, we need to find the vector sum of the velocity vectors of Car A and Car B.
Step 3: Find the angle between the resultant velocity vector and the north direction.
- Once we have the resultant velocity vector, we can find the angle between it and the north direction.
- This angle will be the angle x.
Let's calculate this step by step.
Step 1: Determine the velocity vectors:
- Car A: going north-east at 80 km/h
- This velocity vector can be represented by V_A = 80 km/h at an angle of 45 degrees north of east.
- Car B: going south-east at 60 km/h
- This velocity vector can be represented by V_B = 60 km/h at an angle of 45 degrees south of east.
Step 2: Calculate the resultant velocity vector:
- The resultant velocity vector V_R can be calculated by adding the two velocity vectors V_A and V_B.
- V_R = V_A + V_B
Step 3: Find the angle between the resultant velocity vector and the north direction:
- To find this angle, we can use trigonometry.
- Since the north direction is straight up, we can consider it as the positive y-axis.
- We can find the angle x using the following formula:
x = arctan(V_Ry / V_Rx)
Note: V_Rx and V_Ry represent the x and y components of the resultant velocity vector V_R.
By following these steps, we can find the value of angle x and determine the direction of the relative velocity of Car A with respect to Car B.