a motorcycle is driven 50 km west then 30 km south and 25 km 30 degree west of south show the vector diagram find the total displacement of motorcycle
All angles are measured CW from +y-axis.
Disp. = -50 - 30i + 25[210o] = -50 - 30i + 25*sin210 + (25*cos210)i
Disp. = -50-30i-12.5-21.7i = -62.5 - 51.7i = 81.1km[50.4o] W. of S.
Disp. = 81.1km[230.4o] CW.
draw the vectors and add them up. The final displacement vector is
<-50,0> + <0,-30> + <-25*0.5 , -25*√3/2>
To find the total displacement of the motorcycle, we need to add up the individual displacements in the form of vectors. Let's break down the given information into vectors:
1. First displacement: 50 km west
- This can be represented as a vector (-50 km, 0 km) since the motorcycle travels only in the west direction.
2. Second displacement: 30 km south
- This can be represented as a vector (0 km, -30 km) since the motorcycle travels only in the south direction.
3. Third displacement: 25 km 30 degrees west of south
- To represent this displacement, we need to find the horizontal and vertical components of this vector.
The horizontal component can be found using cos(30°) = √3/2:
- Horizontal Component: 25 km * (√3/2) = (25 km * √3) / 2 ≈ 21.65 km
The vertical component can be found using sin(30°) = 1/2:
- Vertical Component: 25 km * (1/2) = 25 km / 2 = 12.5 km
This displacement can be represented as a vector (-21.65 km, -12.5 km) since it goes to the left (west) and down (south).
Now, let's add up all the vectors to find the total displacement:
Total Displacement = (-50 km, 0 km) + (0 km, -30 km) + (-21.65 km, -12.5 km)
Adding the corresponding components separately:
Total Displacement = (-50 km + 0 km - 21.65 km, 0 km - 30 km - 12.5 km)
Total Displacement = (-71.65 km, -42.5 km)
Therefore, the total displacement of the motorcycle is approximately (-71.65 km, -42.5 km).