A 1900 kg Oldsmobile traveling south on Abbott Road at 13.6 m/s is unable to stop on the ice covered intersection for a red light at Saginaw Street. The car collides with a 3854 kg truck hauling animal feed east on Saginaw at 9.8 m/s. The two vehicles remain locked together after the impact. Calculate the velocity of the wreckage immediately after the impact. Give the speed for your first answer and the compass heading for your second answer.
south momentum = 1900 * 13.6 = 25840
east momentum = 3854 * 9.8 = 37769
same after of course
mass = 1900+3854 = 5754
south momentum = 5754 Vs = 25840
Vs = 4.49 m/s
east momentum = 5754 Ve = 37769
Ve = 6.56 m/s
V = sqrt (Vs^2+Ve^2) = 7.95 m/s
tan angle E of S = Ve/Vs = 6.56/4.49
angle E of S = 55.6
180 - 55.6 = 124 degrees heading or about southeast by east
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To calculate the velocity of the wreckage immediately after the impact, we can use the principles of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision. We can calculate the total momentum before the collision using the formula:
Momentum before collision = (mass of Oldsmobile) × (velocity of Oldsmobile) + (mass of truck) × (velocity of truck)
Momentum before collision = (1900 kg) × (13.6 m/s) + (3854 kg) × (9.8 m/s)
Momentum before collision = 25,840 kg·m/s + 37,759.2 kg·m/s
Momentum before collision = 63,599.2 kg·m/s
Since the two vehicles remain locked together after the impact, the total mass of the wreckage is the sum of the masses of the Oldsmobile and the truck:
Total mass of wreckage = mass of Oldsmobile + mass of truck
Total mass of wreckage = 1900 kg + 3854 kg
Total mass of wreckage = 5754 kg
Therefore, the velocity of the wreckage immediately after the impact can be calculated by dividing the momentum before the collision by the total mass of the wreckage:
Velocity of wreckage = Momentum before collision / Total mass of wreckage
Velocity of wreckage = 63,599.2 kg·m/s / 5754 kg
Velocity of wreckage ≈ 11.06 m/s
So, the speed of the wreckage immediately after the impact is approximately 11.06 m/s.
To determine the compass heading, we need to find the direction of the wreckage's motion. Given that the Oldsmobile was traveling south and the truck was traveling east, the wreckage's motion will be a combination of these two directions, resulting in a diagonal direction. However, without additional information about the collision angle or the direction of motion after the impact, it is not possible to determine the specific compass heading.
To calculate the velocity of the wreckage immediately after the impact, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.
Momentum is defined as the product of an object's mass and velocity. In this case, we have two vehicles involved in a collision, so the total momentum before the impact is equal to the total momentum after the impact.
In the south direction (which is considered positive), the momentum of the Oldsmobile before the impact is given by:
Momentum of Oldsmobile = mass of Oldsmobile * velocity of Oldsmobile
= 1900 kg * 13.6 m/s
In the east direction (which is considered positive), the momentum of the truck before the impact is given by:
Momentum of truck = mass of truck * velocity of truck
= 3854 kg * 9.8 m/s
Since the two vehicles remain locked together after the impact, their combined mass will be the sum of the individual masses:
Total mass of wreckage = mass of Oldsmobile + mass of truck
= 1900 kg + 3854 kg
Now, we can calculate the velocity of the wreckage immediately after the impact using the principle of conservation of momentum:
Total momentum before = Total momentum after
(mass of Oldsmobile * velocity of Oldsmobile) + (mass of truck * velocity of truck) = (total mass of wreckage) * (velocity of wreckage)
Substituting the given values, we have:
(1900 kg * 13.6 m/s) + (3854 kg * 9.8 m/s) = (1900 kg + 3854 kg) * (velocity of wreckage)
Solving this equation will give us the velocity of the wreckage immediately after the impact.