A 1971 kg Oldsmobile traveling west on Saginaw Street at 16.4 m/s is unable to stop on the ice covered intersection for a red light at Abbott Road. The car collides with a 4170 kg truck hauling animal feed south on Abbott at 9.4 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. (remember, the CAPA abbreviation for degrees is deg)
Using x y coordinates: i is unit x vector, j is unit y vector
original momentum = -1971*16.4 i - 4170 * 9.4 j
= -32324 i - 39198 j
final momentum = 6141 Vx i + 6141 j
so
Vx = -32324/6141 = -5.26 or 5.26 m/s west
Vy = -39198/6141 = -6.38 or 6.38 m/s south
v = sqrt (5.26^2+6.38^2)
tan angle south of west = 6.38/5.26 = 1.2
so angle s of w = 50.2
so heading = 270 - 50.2 = 220
To calculate the velocity of the wreckage immediately after the impact, we will use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
The momentum of the Oldsmobile (car) is given by the product of its mass and velocity:
Momentum of car = mass of car × velocity of car
= 1971 kg × 16.4 m/s
The momentum of the truck is given by:
Momentum of truck = mass of truck × velocity of truck
= 4170 kg × 9.4 m/s
After the collision:
The two vehicles remain locked together, so their combined mass will be the sum of the masses of the car and truck:
Total mass after collision = mass of car + mass of truck
= 1971 kg + 4170 kg
Let's calculate the total momentum after the collision using the conservation of momentum principle:
Total momentum before collision = Total momentum after collision
(1971 kg × 16.4 m/s) + (4170 kg × 9.4 m/s) = (1971 kg + 4170 kg) × velocity of wreckage
Now, we can solve this equation to find the velocity of the wreckage immediately after the impact.
Once the velocity is calculated, to find the speed, you can take the magnitude of the velocity vector, which is its absolute value. And to find the compass heading, you can calculate the angle of the velocity vector in relation to a reference direction, usually the north direction (0 degrees).