Question

Two vehicles A and B are traveling west and south, respectively, toward the same intersection where they collide and lock together. Before the collision A (total weight 1870 N) is moving with a speed of 42 m/s and B (total weight 1100 N ) has a speed of 27 m/s. student submitted image, transcription available below A) Find the magnitude of the velocity of the interlocked vehicles after the collision.

Answer 1

The magnitude of the velocity of the interlocked vehicles after the collision is 0.234 m/s.

Step-by-step explanation:

The magnitude of the velocity of the interlocked vehicles after the collision can be calculated using the principles of conservation of momentum. Momentum is a vector quantity and is calculated by multiplying the mass of the object by its velocity. The total momentum before the collision is equal to the total momentum after the collision.

Let the final velocity of the interlocked vehicles be V. The total momentum before the collision is given by:

Total momentum before collision = (mass of vehicle A * velocity of vehicle A) + (mass of vehicle B * velocity of vehicle B)

Plugging in the values:

Total momentum before collision = (1870 N * 42 m/s) + (1100 N * -27 m/s)

According to the principle of conservation of momentum, the total momentum after the collision is equal to the total momentum before the collision. Therefore:

Total momentum after collision = Total momentum before collision

(mass of interlocked vehicles * V) = (1870 N * 42 m/s) + (1100 N * -27 m/s)

Solving for V:

V = ((1870 N * 42 m/s) + (1100 N * -27 m/s)) / (mass of interlocked vehicles)

Plugging in the values:

V = ((1870 N * 42 m/s) + (1100 N * -27 m/s)) / (1870 N + 1100 N)

V = 696 N m/s / 2970 N

V = 0.234 m/s

Therefore, the magnitude of the velocity of the interlocked vehicles after the collision is 0.234 m/s.

Answer 2

To find the magnitude of the velocity of the interlocked vehicles after the collision, we can use the principle of conservation of momentum. After calculating the expression, the velocity of the interlocked vehicles is approximately 35.5 m/s.

Step-by-step explanation:

To find the magnitude of the velocity of the interlocked vehicles after the collision, we can use the principle of conservation of momentum. Since the vehicles collide and lock together, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the momentum of vehicle A is the product of its mass (1870 N) and velocity (42 m/s), and the momentum of vehicle B is the product of its mass (1100 N) and velocity (27 m/s). After the collision, the interlocked vehicles have a combined mass equal to the sum of their individual masses (1870 N + 1100 N) and a combined velocity (v).

Using the conservation of momentum equation: the momentum before the collision ([(mass of A) * (velocity of A)] + [(mass of B) * (velocity of B)]) is equal to the momentum after the collision ([(mass of A + mass of B) * (velocity of the interlocked vehicles)]). We can rearrange the equation to solve for the velocity of the interlocked vehicles after the collision.

[(mass of A) * (velocity of A)] + [(mass of B) * (velocity of B)] = (mass of A + mass of B) * (velocity of the interlocked vehicles)

Substituting the given values into the equation, we have:

(1870 N * 42 m/s) + (1100 N * 27 m/s) = (1870 N + 1100 N) * (velocity of the interlocked vehicles)

Simplifying the equation yields:

[(1870 N * 42 m/s) + (1100 N * 27 m/s)] / (1870 N + 1100 N) = (velocity of the interlocked vehicles)

Calculating the expression results in a velocity of approximately 35.5 m/s for the interlocked vehicles after the collision.