2. Two pickup trucks crash at a 90 degree intersection. If the momentum of pickup A is
4.60 x10^4 kg km/h north and the momentum of pickup B is 6.25 x 10^4 kg km/h
east, what is the magnitude of the resulting momentum of the final mass?
Resulting momentum:
M1*V1 + M2*V2 = 4.60*10^4i + 6.25*10^4.
Tan A = Y/X =4.60*10^4/6.25*10^4 = 0.736, A = 36.4o
Res. Momentum = X/Cos36.4 = 6.25*10^4/Cos36.4 = 7.76*10^4 kg km/h.
Remember that the total momentum
before the collision = The total momentum after the collision.
To find the magnitude of the resulting momentum of the final mass after the collision, we need to use the concept of vector addition.
First, we need to break down the momenta of the two pickup trucks into their respective components, one along the north-south axis (vertical) and the other along the east-west axis (horizontal).
Given:
Momentum of pickup A: 4.60 x 10^4 kg km/h north
Momentum of pickup B: 6.25 x 10^4 kg km/h east
Next, we convert the given momenta from km/h to m/s by dividing by 3.6 since 1 km/h = 1000 m / 3600 s = 1/3.6 m/s.
Momentum of pickup A in m/s:
4.60 x 10^4 kg km/h / 3.6 = 12.78 x 10^3 kg m/s north
Momentum of pickup B in m/s:
6.25 x 10^4 kg km/h / 3.6 = 17.36 x 10^3 kg m/s east
Now we have the momentum components along the north and east directions: A_north = 12.78 x 10^3 kg m/s and B_east = 17.36 x 10^3 kg m/s.
To find the total momentum after the collision, we need to add these two momentum vectors together. Since they are perpendicular to each other, we can use the Pythagorean theorem.
Magnitude of the resulting momentum (final mass) = sqrt((A_north^2 + B_east^2))
Plugging in the given values:
Magnitude of the resulting momentum = sqrt((12.78 x 10^3)^2 + (17.36 x 10^3)^2)
Simplifying this equation will give us the magnitude of the resulting momentum of the final mass after the collision.