Joseph drives his car 10 km [E20 °S] then 25 km[N]. What is his total displacement?
To find the total displacement of Joseph's car, we need to consider both the distance traveled and the direction.
In this case, Joseph first drives 10 km towards the east at an angle of 20° south of the east (E20 °S). Then, he drives 25 km directly towards the north.
To determine the net displacement, we can break down the distances into their respective horizontal (east-west) and vertical (north-south) components.
First, let's find the horizontal displacement:
The 10 km distance towards the east forms the base of a right-angled triangle. The angle, E20 °S, indicates that the direction is measured from the south towards the east. Thus, the horizontal component can be found using trigonometry.
Horizontal component = 10 km * cos(20°)
Next, let's find the vertical displacement:
The 25 km distance towards the north represents the height of a right-angled triangle. Since there is no angle given, we can assume that it is perpendicular to the ground and represents the vertical displacement.
Now, to find the total displacement, we can use these horizontal and vertical components to calculate the distance and direction of the resulting displacement.
Horizontal displacement: 10 km * cos(20°)
Vertical displacement: 25 km
To calculate the total displacement, we use the Pythagorean theorem:
Total Displacement = √(Horizontal^2 + Vertical^2)
Total Displacement = √((10 km * cos(20°))^2 + (25 km)^2)
By evaluating this equation, you will find the total displacement of Joseph's car.