A car of mass 422 kg is moving 36.0° North of East at a speed of 15.4 m/s. What is the magnitude of the momentum of the car? (magnitude - how big is it? ignore direction). What is the east-west component of the momentum of the car?
I already figured out the first question but can't figure out the last. Please help! Thanks
mv cos36
To calculate the east-west component of the momentum of the car, you need to find the horizontal component of its velocity. This requires breaking down the velocity vector into its horizontal and vertical components.
First, let's find the vertical component. The car is moving at an angle of 36.0° North of East, which means the vertical component of its velocity is given by:
vertical velocity = velocity * sin(angle)
vertical velocity = 15.4 m/s * sin(36.0°)
vertical velocity ≈ 9.37 m/s
Next, let's find the horizontal component. The car is moving at an angle of 36.0° North of East, which means the horizontal component of its velocity is given by:
horizontal velocity = velocity * cos(angle)
horizontal velocity = 15.4 m/s * cos(36.0°)
horizontal velocity ≈ 12.37 m/s
Now, we have the horizontal component of the car's velocity, which represents the east-west direction.
Finally, to find the east-west component of the momentum, we multiply the horizontal component of the velocity by the mass of the car:
east-west component of momentum = horizontal velocity * mass
east-west component of momentum = 12.37 m/s * 422 kg
east-west component of momentum ≈ 5,221.14 kg·m/s
Therefore, the east-west component of the momentum of the car is approximately 5,221.14 kg·m/s.