A car with mass m is traveling west

A) Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j.

B) How far, in meters, will the vehicles slide after the collision?

Answer:- 

1. The velocity of the system after the collision can be expressed as follows:

v = (m_c * v_c + m_t * v_t)/(m_c + m_t)

where

• v is the velocity of the system after the collision
• m_c is the mass of the car
• v_c is the velocity of the car before the collision
• m_t is the mass of the truck
• v_t is the velocity of the truck before the collision

Plugging in the values from the problem statement, we get:

v = (1225 kg * 9.5 m/s + 1654 kg * 8.6 m/s)/(1225 kg + 1654 kg)

v = 12.1 m/s

The direction of the velocity can be found using the following equation:

tan(theta) = (v_t)/(v_c)

where

• theta is the angle between the velocity of the system after the collision and the x-axis
• v_t is the velocity of the truck before the collision
• v_c is the velocity of the car before the collision

Plugging in the values from the problem statement, we get:

tan(theta) = (8.6 m/s)/(9.5 m/s)

theta = 37.0 degrees

Therefore, the velocity of the system after the collision is 12.1 m/s at an angle of 37.0 degrees west of north.

1. The distance that the vehicles will slide after the collision can be found using the following equation:

d = (v^2)/(2 * μ * g)

where

• d is the distance that the vehicles will slide
• v is the velocity of the system after the collision
• μ is the coefficient of friction
• g is the acceleration due to gravity

Plugging in the values from the problem statement, we get:

d = (12.1 m/s)^2 / (2 * 0.5 * 9.8 m/s^2)

d = 7.5 meters

Therefore, the vehicles will slide 7.5 meters after the collision.