A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30 degrees east of north for 25 km. Sketch the vector diagram and determine a) the magnitude and b) the angle of the car's total displacement from its starting point

To determine the car's total displacement, we need to find the resultant vector by adding the individual vectors corresponding to each leg of the journey. Let's break down the information provided:

1. The car is driven east for a distance of 50 km. This corresponds to a vector of magnitude 50 km in the east direction.

2. The car then goes north for a distance of 30 km. This corresponds to a vector of magnitude 30 km in the north direction.

3. Finally, the car moves in a direction 30 degrees east of north for 25 km. This corresponds to a vector of magnitude 25 km.

To sketch the vector diagram, draw a horizontal line representing the east direction, a vertical line representing the north direction, and label the appropriate distances along each line. Starting from the origin (the car's starting point), draw the vectors corresponding to each leg of the journey. The vector in the east direction should be 50 units long, the vector in the north direction should be 30 units long, and the vector east of north should be 25 units long at an angle of 30 degrees.

To determine the magnitude and angle of the car's total displacement, we can use trigonometry. We'll consider the horizontal (east) and vertical (north) components of the resultant vector separately:

1. Horizontal component: The eastward vector of 50 km contributes to the horizontal displacement. Since there are no other vectors involved in the east direction, the horizontal component of the displacement is 50 km.

2. Vertical component: The northward vector of 30 km and the east of north vector of 25 km contribute to the vertical displacement. We need to find the vertical component of the vector east of north. Using trigonometry, the vertical component is given by 25 km * sin(30 degrees) = 12.5 km.

Now, we can find the magnitude (total displacement) and angle using the horizontal and vertical components:

a) Magnitude: The magnitude of the total displacement is given by the Pythagorean theorem:

Magnitude = sqrt((horizontal component)^2 + (vertical component)^2)

Magnitude = sqrt((50 km)^2 + (12.5 km)^2)

Magnitude ≈ 51.26 km

b) Angle: The angle of the total displacement can be found using trigonometry:

Angle = arctan(vertical component / horizontal component)

Angle = arctan(12.5 km / 50 km)

Angle ≈ 14.04 degrees

Therefore, the car's total displacement from its starting point is approximately 51.26 km at an angle of approximately 14.04 degrees north of east.

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north

west--|--east
south
on your vector diagram draw a line going east(right) mark 50km the 30km north(up) for 30degrees east of north imagine a line going straight up(north) then measure 30degreese towards where east would be and make the line 25km

once you've drawn the vector diagram you should be able to work out part b