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A 1400 kg car moving north at 24.0 m/s collides with a 2200 kg car moving east at 18.0 m/s. The
two cars stick together after the collision. What is the speed and direction of the two cars after
the collision?

2 Answers

3 votes

Final answer:

After a completely inelastic collision, the two cars move together at a speed of approximately 14.43 m/s at an angle of 40.2° north of east, determined by conservation of momentum and vector addition.

Step-by-step explanation:

The question pertains to the calculation of the final velocity and direction of two cars after a collision, using the principles of conservation of momentum. Since the two cars stick together after the collision, this is an example of a completely inelastic collision. To find the speed and direction of the cars after the collision, we can apply the conservation of linear momentum separately in the north-south and east-west directions.

First, we calculate the momentum of each car before the collision:

1400 kg car (northward): p1 = m1 * v1 = 1400 kg * 24.0 m/s = 33600 kg*m/s northward

2200 kg car (eastward): p2 = m2 * v2 = 2200 kg * 18.0 m/s = 39600 kg*m/s eastward

Since the cars stick together, their combined mass is m_total = 1400 kg + 2200 kg = 3600 kg.

Using vector addition, we calculate the combined momentum vector:

p_total = sqrt((33600^2) + (39600^2)) = sqrt(1131360000 + 1568160000) = sqrt(2699520000) = 51957 kg*m/s

For the direction, we calculate the angle θ with the east axis using arctan(northward momentum / eastward momentum):

θ = arctan(33600/39600) = arctan(0.8485) ≈ 40.2° north of east

Finally, we find the speed of the cars after the collision by dividing the total momentum by the total mass:

Speed after collision = p_total / m_total = 51957 kg*m/s / 3600 kg ≈ 14.43 m/s

Hence, the two cars move together at a speed of approximately 14.43 m/s at an angle of 40.2° north of east after the collision.

User Yacon
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6.7k points
3 votes
Both cars will be stopped do you the speed and force due to the mass of each car since they both basically cancel each other out they both will be stopped in a real life
User Rodrigo Leite
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6.8k points