A motorcycle is driven west for a distance of 50 km, then south for 30 km, and then in a direction 30° west of south for 25 km. Find the total displacement of the motorcycle from its starting point.
To find the total displacement of the motorcycle from its starting point, we need to find the net displacement. We can break down the displacements into their x and y components and then add them up.
Let's assume the starting point as the origin (0,0).
1. The motorcycle is driven west for 50 km. This corresponds to a displacement of -50 km in the x-direction (west) and no displacement in the y-direction. So the displacement is (-50, 0).
2. The motorcycle is then driven south for 30 km. This corresponds to a displacement of 0 km in the x-direction and -30 km in the y-direction (south). So the displacement is (0, -30).
3. Finally, the motorcycle is driven in a direction 30° west of south for 25 km. To find the x and y components of this displacement, we can use trigonometry. The angle is given as 30° west of south, which means it is 60° below the negative y-axis. The length of this displacement is given as 25 km.
The x-component of this displacement is calculated as cos(60°) * 25 km = -12.5 km.
The y-component of this displacement is calculated as sin(60°) * 25 km = -21.65 km (approximated).
So the displacement for this step is approximately (-12.5, -21.65).
Now we can add up all the displacements to find the net displacement:
Net displacement = (-50, 0) + (0, -30) + (-12.5, -21.65)
Adding the x-components, we get: -50 + 0 - 12.5 = -62.5 km
Adding the y-components, we get: 0 - 30 - 21.65 = -51.65 km (approximated)
So, the total displacement of the motorcycle from its starting point is approximately (-62.5, -51.65).