A car travels 1.46 km in the x-direction, then turns left 74.8 ◦ to the original direction and travels an additional distance of 2.57 km. Calculate the x component of the car's net displacement.

The x component of the car's net displacement = 3.94 km

Explanation:

A car travels 1.46 km in the x-direction, which means displacement = 1.46 i km.

Then car turns left 74.8⁰ to the original direction and travels an additional distance of 2.57 km, which means displacement = 2.57 cos 74.8⁰ i + 2.57 sin 74.8⁰ = (2.48 i + 0.67 j) km

So total displacement = 1.46 i + 2.48 i + 0.67 j = (3.94 i + 0.67 j) km

The x component of the car's net displacement = 3.94 km