Answer:
Question
A. Find the total momentum of the system
B. Find the magnitude of the total momentum
Step-by-step explanation:
Momentum can be defined as the product of mass and velocity, it is a vector quantity.
Momentum = mass × velocity
P = mv
So, since it is a vector quantity we must take note of its direction
Given that,
1. 26-kg dog is running northward at 2.7 m/'s
Md = 26kg
Vy = 2.7m/s •j
Then, it is moving in the positive y direction
Then, it is momentum is
Py = Md•Vy
Py = 26 × 2.7 •j
Py = 70.2 kgm/s •j
2. A 5.3 kg cat is running eastward at 3.0 m/s.
The cat is running towards the east, then it is moving in the positive x direction
Vx = 3 •i m/s
Mc = 5.3kg
Px = Mc•Vx
Px = 5.3 × 3 •i
Px = 15.9 •i kgm/s
Then,
Total momentum is equal to
P = Px + Py
P = 15.9 •i + 70.2 •j kgm/s
B. Magnitude of the total momentum
Magnitude of a vector quantity
x = a•i + b•j is generally given as
X = √(a²+b²)
Direction <X = arctan(b/a)
Therefore,
|P| = √(15.9²+70.2²)
|P| = 71.98 kgm/s
Direction
<P = arctan(Py/Px) =arctan(70.2/15.9)
<P = 77.24°