Question

A cyclist rides 5.0 km due east, then 10.0 km 20° west of north. From this point she rides 8.0 km due west. What is the final displacement from where the cyclist started?

a) Option a: Displacement = (4.8ˆi + 12.7ˆj) km; Option b: Displacement = (-4.8ˆi - 12.7ˆj) km
b) Option a: Displacement = (15.2ˆi + 7.3ˆj) km; Option b: Displacement = (-15.2ˆi - 7.3ˆj) km
c) Option a: Displacement = (12.7ˆi + 4.8ˆj) km; Option b: Displacement = (-12.7ˆi - 4.8ˆj) km
d) Option a: Displacement = (7.3ˆi + 15.2ˆj) km; Option b: Displacement = (-7.3ˆi - 15.2ˆ j) km

Answer 1

The final displacement of the cyclist is -3.0ˆi + 9.40ˆj km.

Step-by-step explanation:

To solve this problem, we can break down the cyclist's movements into components using vectors. The cyclist rides 5.0 km due east, so the displacement in the x-direction is 5.0 km and there is no displacement in the y-direction. Next, the cyclist rides 10.0 km 20° west of north. We can split this displacement into x and y components using trigonometry.

The x-component is 10.0 km * sin(20°) = 3.42 km.

The y-component is 10.0 km * cos(20°) = 9.40 km.

Finally, the cyclist rides 8.0 km due west, so the displacement in the x-direction is -8.0 km and there is no displacement in the y-direction.

To find the final displacement, we add up the x and y components:

(5.0 km + (-8.0 km))ˆi + (0 km + 9.40 km)ˆj = (-3.0ˆi + 9.40ˆj) km.

Therefore, the correct option is:

Option b: Displacement = (-3.0ˆi + 9.40ˆj) km.