Two balls undergo inelastic collision. The y-momentum after the collision is 98 kilogram meters/second, and the x-momentum after the collision is 100 kilogram meters/second. What is the magnitude of the resultant momentum after the collision?
p=sqrt{p(x)² +p(y)²} =
= sqrt(98² +100²)=140 kg•m/s
v = Sqrt(v1^2 + v2^2)
v = sqrt(98^2 + 100^2)
V = 140.01
V = 1.4 * 10^2
To find the magnitude of the resultant momentum after the collision, we can use the Pythagorean theorem.
Let's denote the magnitude of the resultant momentum as R, the x-momentum as Px, and the y-momentum as Py.
Given:
Px = 100 kg·m/s
Py = 98 kg·m/s
Using the Pythagorean theorem, we have:
R^2 = Px^2 + Py^2
Substituting the given values, we get:
R^2 = (100 kg·m/s)^2 + (98 kg·m/s)^2
Calculating the square of each term:
R^2 = 10000 kg^2·m^2/s^2 + 9604 kg^2·m^2/s^2
R^2 = 19604 kg^2·m^2/s^2
Taking the square root of both sides:
R = √(19604 kg^2·m^2/s^2)
Simplifying:
R = 140 kg·m/s
Therefore, the magnitude of the resultant momentum after the collision is 140 kilogram meters/second.
To find the magnitude of the resultant momentum after the collision, we can use the Pythagorean theorem since we have the y-momentum and x-momentum.
The Pythagorean theorem states that the square of the magnitude of a vector (in this case, momentum) is equal to the sum of the squares of its components. Mathematically, it can be expressed as:
Magnitude^2 = y-momentum^2 + x-momentum^2
Plugging in the given values:
Magnitude^2 = 98^2 + 100^2
Magnitude^2 = 9604 + 10000
Magnitude^2 = 19604
To find the magnitude, we take the square root of both sides:
Magnitude = √19604
By evaluating the square root of 19604, we find:
Magnitude ≈ 139.95 kilogram meters/second
Therefore, the magnitude of the resultant momentum after the collision is approximately 139.95 kilogram meters/second.