INFORMATION:
Kathy and Bill collided at an intersection. The police learned the mass of the truck is 3200 kg and the mass of the car is 2800 kg. Based on the length of the skid marks at the scene and the mass of the vehicles, police estimate that the combined mass was moving at 7.0 m/s just after the impact. From this point, that two vehicles slid and came to rest at the corner of the intersection.
Using the principle of conservation of momentum, the police determined that Bill's truck was travelling at 2.3 m/s before the collision, and Kathy's car was travelling at 15 m/s before the collision.
The two momentum vectors before the collision are represented by the horizontal and vertical lines in the diagram below. The momentum after the collision is the slanted line. Adding the two momentum vectors before the collision equals the momentum after the collision, according to the law of conservation of momentum.
3) Using the vector diagram above and your calculated value for the momentum of the combined vehicles, verify the police's calculations and determine the momentum and velocity of Bill's truck just before the collision.
4)Using the vector diagram above and your calculated value for the momentum of the combined vehicles, verify the police's calculations and determine the momentum and velocity of Cathy's car just before the collision.
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To verify the police's calculations and determine the momentum and velocity of Bill's truck just before the collision, we need to use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. In this case, the combined momentum of the truck and the car just after the impact is given as 7.0 m/s.
Let's assume that the momentum of the truck just before the collision is represented by the vector A in the diagram, and the momentum of Kathy's car just before the collision is represented by the vector B.
According to the law of conservation of momentum, the sum of vector A and vector B should equal the momentum vector after the collision (represented by the slanted line in the diagram).
To determine the momentum and velocity of Bill's truck just before the collision, we can use the following steps:
1. Calculate the magnitude of vector B (momentum of Kathy's car just before the collision). Given that the combined momentum just after the collision is 7.0 m/s, we can subtract the magnitude of vector B from this value. Let's assume the magnitude of vector B is M_b.
Combined momentum just after the collision = M_a + M_b
M_a + M_b = 7.0 m/s
2. Calculate the magnitude of vector A (momentum of Bill's truck just before the collision). Given that the mass of the truck is 3200 kg, we can use the formula: M_a = m_a * v_a, where m_a is the mass of the truck and v_a is the velocity of the truck just before the collision.
3. Rearrange the equation from step 1 to solve for M_a:
M_a = 7.0 m/s - M_b
4. Plug in the value of M_a obtained in step 3 into the equation from step 2 and solve for v_a:
M_a = m_a * v_a
With this calculated value for the momentum and velocity of Bill's truck just before the collision, you can verify the police's calculations.
To determine the momentum and velocity of Kathy's car just before the collision, you can follow the same steps using the given information for the mass of the car (2800 kg), the combined momentum just after the collision (7.0 m/s), and the velocity of Kathy's car just before the collision (15 m/s).