Kelly is driving a car with a mass of 800 kilograms in a south direction with a speed of 18 meters/second. Dominic is driving a truck with a mass of 1500 kilograms with a velocity of 15 meters/second to the east. They undergo perfectly inelastic collision. What is the magnitude of the final momentum of both the truck and the car.
A. 7.0 × 104 kilogram meters/second
B. 3.2 × 104 kilogram meters/second
C. 2.4 × 104 kilogram meters/second
D. 3.7 × 104 kilogram meters/second
E. 3.4 × 104 kilogram meters/second
final momentum= initial momentum
magnitude initial= sqrt((800*18)^2+(1500*15)^2 )
This is impossible.
no
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To find the magnitude of the final momentum of both the truck and the car after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. The formula for momentum is:
Momentum = mass × velocity
Before the collision, Kelly's car has a momentum of:
Momentum of car = 800 kg × 18 m/s = 14,400 kg·m/s (to the south)
Dominic's truck has a momentum of:
Momentum of truck = 1500 kg × 15 m/s = 22,500 kg·m/s (to the east)
To find the total momentum before the collision, we need to calculate the vector sum of these two momenta. Since they are at right angles to each other, we can use the Pythagorean theorem:
Total momentum before collision = √(Momentum of car)^2 + (Momentum of truck)^2
Total momentum before collision = √((14,400 kg·m/s)^2 + (22,500 kg·m/s)^2)
Total momentum before collision = √(207,360,000 + 506,250,000) kg^2·m^2/s^2
Total momentum before collision = √713,610,000 kg^2·m^2/s^2
Total momentum before collision ≈ 26,720.051 kg·m/s
Now, since the collision is perfectly inelastic, the two vehicles stick together after the collision. This means they move as a single unit with a combined mass. The final momentum of the vehicle after the collision will be equal to the total momentum before the collision.
Therefore, the magnitude of the final momentum of both the truck and the car is approximately 26,720.051 kg·m/s.
None of the given options match this value, so none of the provided answers is correct.