A car heads due west on Interstate 80 going 63.0 km/hr for 2.1 hours. The car then turns and heads exactly northwest on Interstate 42 going 53 km/hr for 3.3 hours. What is the resultant displacement of the car?

To find the resultant displacement of the car, we need to determine the total distance traveled in each direction and then calculate the net displacement.

First, let's calculate the distance traveled in the westward direction:

Distance = Speed * Time
Distance = 63.0 km/hr * 2.1 hours
Distance = 132.3 km

Now, let's calculate the distance traveled in the northwest direction. The northwest direction can be broken down into two perpendicular components: north and west.

The distance traveled north is given by:

Distance_north = Speed_north * Time
Speed_north is the component of the speed in the north direction, which can be calculated as:
Speed_north = Speed * sin(45°)
Note: We assume a 45 degrees angle for the northwest direction, as it is exactly midway between north and west.

Speed_north = 53 km/hr * sin(45°)
Speed_north ≈ 37.53 km/hr

Distance_north = Speed_north * Time
Distance_north = 37.53 km/hr * 3.3 hours
Distance_north ≈ 123.87 km

Similarly, the distance traveled westwards is given by:

Distance_west = Speed_west * Time
Speed_west is the component of the speed in the west direction, which can be calculated as:
Speed_west = Speed * cos(45°)

Speed_west = 53 km/hr * cos(45°)
Speed_west ≈ 37.53 km/hr

Distance_west = Speed_west * Time
Distance_west = 37.53 km/hr * 3.3 hours
Distance_west ≈ 123.87 km

Now, let's calculate the net displacement using the Pythagorean theorem, as the north and west displacements form a right triangle:

Displacement^2 = Distance_north^2 + Distance_west^2
Displacement^2 = 123.87 km^2 + 123.87 km^2
Displacement^2 ≈ 30644.4569 km^2

Taking the square root of both sides, we get:

Displacement ≈ √30644.4569 km^2
Displacement ≈ 175.02 km

Therefore, the resultant displacement of the car is approximately 175.02 km.