Horizontal Displacement of a Car Traveling Northeast

What is the horizontal displacement of a car that travels 75 km in a direction 45° northeast?

a) 45 km

b) 53 km

c) 75 km

d) 150 km

Answer:

The horizontal displacement of a car traveling 75 km in a 45° northeast direction is approximately 53 km.

The horizontal displacement of a car that travels 75 km in a direction 45° northeast can be calculated using trigonometry. Since the car is moving in a diagonal direction, we can break down the displacement into its horizontal and vertical components. The horizontal displacement can be found by using the cosine function.

Given that the displacement is 75 km and the angle is 45°, we can use the formula:

Horizontal displacement = displacement * cos(angle)

Horizontal displacement = 75 km * cos(45°)

Horizontal displacement = 75 km * 0.7071

Horizontal displacement = 53.03 km

Therefore, the horizontal displacement of the car is approximately 53 km.