1.Two motorcycles of equal mass collide at a 90 degree intersection. If the momentum of motorcycle A is 450 kg km/h west and the momentum of motorcycle B is 725 kg km/h
south, what is the magnitude of the resulting momentum of the final mass?
sqrt(450^2+725^2)
Hey - you are asking the same question over and over with different numbers.
First you want to know the method ,so you can do all the questions easily.
To find the magnitude of the resulting momentum of the final mass, we need to add the momentum vectors of motorcycle A and motorcycle B using vector addition.
First, let's convert the momenta from kilometers per hour to meters per second, which is the standard SI unit for momentum. We can do this by using the following conversion factors:
1 kilometer = 1000 meters
1 hour = 3600 seconds
For motorcycle A:
Momentum of motorcycle A = 450 kg km/h west
Converting to meters per second:
450 km/h * (1000 m/km) * (1 h/3600 s) = 450 * 1000 / 3600 m/s = 125 m/s (west)
For motorcycle B:
Momentum of motorcycle B = 725 kg km/h south
Converting to meters per second:
725 km/h * (1000 m/km) * (1 h/3600 s) = 725 * 1000 / 3600 m/s = 201.39 m/s (south)
Now, we have the two momentum vectors:
Motorcycle A: 125 m/s (west)
Motorcycle B: 201.39 m/s (south)
To add these vectors, we can use vector addition by considering their components separately. The x-component (west-east direction) and y-component (south-north direction) of the resulting momentum vector are obtained by adding the corresponding components of the initial momenta.
x-component (west-east direction):
Net x-momentum = Momentum of A (west) + Momentum of B (0 since B's momentum is in the south direction) = 125 m/s + 0 m/s = 125 m/s
y-component (south-north direction):
Net y-momentum = Momentum of A (0 since A's momentum is in the west direction) + Momentum of B (south) = 0 m/s + 201.39 m/s = 201.39 m/s
Now, we have the x and y components of the resulting momentum vector:
x-component = 125 m/s
y-component = 201.39 m/s
To find the magnitude of the resulting momentum, we can use the Pythagorean theorem:
Magnitude = sqrt((x-component)^2 + (y-component)^2)
Magnitude = sqrt((125 m/s)^2 + (201.39 m/s)^2)
Magnitude = sqrt(15625 m^2/s^2 + 40557.0721 m^2/s^2)
Magnitude = sqrt(56182.0721 m^2/s^2)
Magnitude = 237.03 m/s
Therefore, the magnitude of the resulting momentum of the final mass is approximately 237.03 m/s.