Question

A 1300 kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2400 kg suv traveling from east to west. the two cars become enmeshed due to the impact and slide as one thereafter. on-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.7, and the cars slide to a halt at a point 6.0 m west and 10.0 m south of the impact point. what is the direction and magnitude of the displacement of the two cars system sliding as one right after the collision? give the direction in degrees in south of west.

Answer 1

The displacement of the two cars system sliding as one right after the collision is approximately 11.66 m and the direction is approximately 56.31° south of west.

Step-by-step explanation:

When the two cars collide and become enmeshed, they slide as one due to the coefficient of kinetic friction between the tires and the pavement. The final displacement of the combined cars can be calculated using the Pythagorean theorem. The displacement is the vector sum of the distances traveled by the cars in the west and south directions.

Using the given measurements, the westward displacement is 6.0 m and the southward displacement is 10.0 m. Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the magnitude of the displacement as follows:

Displacement = √(6.0^2 + 10.0^2) = √(36.0 + 100.0) = √136.0 = 11.66 m

The direction of the displacement can be found using trigonometry. The angle south of west is given by:

Angle = tan^-1(10.0/6.0) = tan^-1(1.67) = 56.31°

Therefore, the magnitude of the displacement is approximately 11.66 m and the direction of the displacement is approximately 56.31° south of west.