If a man travels 5km,40 degree west of north , then 8km east,find the resultant displacement
North: 5cos40
E: 4 sin40+8
Both Mrs. Smith and Mrs. Jones had babies the same day in the same hospital. Mrs. Smith took home a baby girl, whom she named Shirley. Mrs. Jones took home a baby girl, whom she named Jane. Mrs. Jones began to suspect, however, that her child had been accidentally switched with the Smith baby in the nursery. Blood tests were made; Mr. Smith was type A, Mrs. Smith was type B, Mr. Jones was type A, Mrs. Jones was type A, Shirley was type O, and Jane was type B. Had a mix-up occurred?
All angles are measured CCW from +x-axis.
Disp. = 5km[130o] + 8km[0o].
X = 5*Cos130 + 8*Cos0 = -3.21 + 8 = 4.78 km.
Y = 5*sin130 + 8*sin0 = 3.83 + 0 = 3.83 km.
Disp. = 4.78 + 3.83i = 6.113 km[38.70].
I needed a pitagorus theory
To find the resultant displacement, we can use vector addition. First, let's break down the given information into its components.
1. The man travels 5 km 40 degrees west of north. This means that the displacement can be broken down into two components:
- North component: 5 km * cos(40°)
- West component: 5 km * sin(40°)
2. The man then travels 8 km east. This is a simple displacement along the east direction.
To find the resultant displacement, we need to add the north component, subtract the west component, and finally add the east component.
Let's calculate the north and west components:
- North component = 5 km * cos(40°) = 5 km * 0.766 = 3.83 km
- West component = 5 km * sin(40°) = 5 km * 0.643 = 3.21 km
Now, let's calculate the resultant displacement:
Resultant displacement = (3.83 km - 3.21 km) east + 8 km east
= 0.62 km east + 8 km east
= 8.62 km east
Therefore, the resultant displacement is 8.62 km east.