Respuesta :
Answer:
Change in momentum is [tex]2.667\times 10^{4} kg.m/s[/tex]
Solution:
The momentum of any body is the product of its mass and the velocity associated with the body and is generally given by:
[tex]\vec{p} = m\vec{v}[/tex]
Now, as per the question:
Mass of the car, M = 1500 kg
The velocity in the east direction, [tex]v\hat{i} = 40\hat{i} km/h[/tex]
The velocity in the north direction, [tex]v\hat{j} = 50\hat{j} km/h[/tex]
Now, the momentum of the car in the east direction:
[tex]p\hat{i} = mv\hat{i} = 1500\times 40\hat{i} = 60000\hat{i} kg.km/h[/tex]
Now, the momentum of the car in the north direction:
[tex]p\hat{j} = mv\hat{j} = 1500\times 50\hat{j} = 75000\hat{j} kg.km/h[/tex]
Change in momentum is given by:
[tex]\Delta p = p\hat{i} - p\hat{j} = 60000\hat{i} - 75000\hat{j}[/tex]
Now,
[tex]|\Delta p| = |60000\hat{i} - 75000\hat{j}|[/tex]
[tex]|\Delta p| = \sqrt{60000^{2} + 75000^{2}}[/tex]
[tex]|\Delta p| = 96046 kg.km/hr = \frac{96046}{3.6} = 2.667\times 10^{4} kg.m/s[/tex]
(Since, [tex]1kg.km/h = \frac{1}{3.6} kg.m/s[/tex])
