Mary is driving a car of mass 900 kilograms toward the north with a velocity of 22 meters/second. Danny is driving his 900-kilogram car with a velocity of 15 meters/second toward the east. They collide and both cars move together afterwards. What is the magnitude of the resultant momentum of the cars after the collision?
To find the magnitude of the resultant momentum of the cars after the collision, we need to consider the concept of momentum and the principle of conservation of momentum.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, momentum can be written as:
p = m * v
To find the total momentum after the collision, we simply need to add the individual momenta of the two cars. Since the cars move together after the collision, their final velocity will be the same.
The momentum of Mary's car (car A) can be calculated as:
momentum(A) = mass(A) * velocity(A)
Given that the mass (m) of car A is 900 kilograms and its velocity (v) is 22 meters/second, we have:
momentum(A) = 900 kg * 22 m/s
Similarly, the momentum of Danny's car (car B) can be calculated as:
momentum(B) = mass(B) * velocity(B)
Given that the mass (m) of car B is also 900 kilograms and its velocity (v) is 15 meters/second, we have:
momentum(B) = 900 kg * 15 m/s
To find the total momentum after the collision, we add the individual momenta of the two cars:
resultant momentum = momentum(A) + momentum(B)
Substituting the calculated values, we have:
resultant momentum = (900 kg * 22 m/s) + (900 kg * 15 m/s)
Now, calculate the resultant momentum using the provided values.
To find the magnitude of the resultant momentum after the collision, we need to calculate the total momentum before and after the collision.
1. Calculate the momentum of Mary's car before the collision:
Momentum = Mass * Velocity
Momentum = 900 kg * 22 m/s = 19,800 kg·m/s (toward the north)
2. Calculate the momentum of Danny's car before the collision:
Momentum = Mass * Velocity
Momentum = 900 kg * 15 m/s = 13,500 kg·m/s (toward the east)
3. After the collision, the two cars move together. The momentum after the collision will be the sum of their individual momenta before the collision.
Resultant Momentum = Momentum of Mary's car + Momentum of Danny's car
Resultant Momentum = 19,800 kg·m/s (north) + 13,500 kg·m/s (east)
4. To find the magnitude of the resultant momentum, we can use the Pythagorean theorem:
Magnitude of Resultant Momentum = sqrt( (Resultant Momentum)^2 )
Magnitude of Resultant Momentum = sqrt( (19,800 kg·m/s)^2 + (13,500 kg·m/s)^2 )
Magnitude of Resultant Momentum ≈ sqrt(392,040,000 + 182,250,000)
Magnitude of Resultant Momentum ≈ sqrt(574,290,000)
Magnitude of Resultant Momentum ≈ 23,965.8 kg·m/s
Therefore, the magnitude of the resultant momentum of the cars after the collision is approximately 23,965.8 kg·m/s.
They are at 90 degrees to each other.
momentum mary=900*22^2
momentum Danny=900*15^2
resulatant=sqrt(danny^2 + mary^2)
= 900(sqrt(15^2+22^2)