<u>The answer is not contained detail explanation, just a solution and the required values. </u>
All the details are in the pictures, the answers are marked with orange colour.
Note,
in the task no 20.:

V - the velocity of the pair of the balls after collision.
in the task no 21:
m₁ - the mass of the copper ball; m₂ - the mass of the copper calorimeter; m₃ - the mass of the water; t₀ - the initial temperature of water in the copper calorimeter; θ - the final temperature in the calorimeter after the copper ball is transferred into a copper calorimeter; t₁ - the required initial temperature of the copper ball before it is transferred into the calorimeter.
<h3>
Answer:</h3>
209.236 kg · m/s
<h3>
General Formulas and Concepts:</h3>
<u>Math</u>
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Physics</u>
<u>Momentum</u>
Momentum Formula: P = mv
- P is momentum (in kg · m/s)
- m is mass (in kg)
- v is velocity (in m/s)
<h3>
Explanation:</h3>
<u>Step 1: Define</u>
m₁ = 87.2 kg
v₁ = 2.87 m/s
m₂ = 0.0520 kg
v₂ = 789 m/s
<u>Step 2: Find Momentums</u>
<em>Football Player</em>
- Substitute [MF]: P = (87.2 kg)(2.87 m/s)
- Multiply: P = 250.264 kg · m/s
<em>Bullet</em>
- Substitute [MF]: P = (0.0520 kg)(789 m/s)
- Multiply: P = 41.028 kg · m/s
<u>Step 3: Find difference</u>
- Define equation: P₁ - P₂
- Substitute: 250.264 kg · m/s - 41.028 kg · m/s
- Subtract: 209.236 kg · m/s
vector A has magnitude 12 m and direction +y
so we can say

vector B has magnitude 33 m and direction - x

Now the resultant of vector A and B is given as

now for direction of the two vectors resultant will be given as


so it is inclined at 160 degree counterclockwise from + x axis
magnitude of A and B will be


so magnitude will be 35.11 m
vf = 10 m/s. A ball with mass of 4kg and a impulse given of 28N.s with a intial velocity of 3m/s would have a final velocity of 10 m/s.
The key to solve this problem is using the equation I = F.Δt = m.Δv, Δv = vf - vi.
The impulse given to the ball with mass 4Kg is 28 N.s. If the ball were already moving at 3 m/s, to calculate its final velocity:
I = m(vf - vi) -------> I = m.vf - m.vi ------> vf = (I + m.vi)/m ------> vf = I/m + vi
Where I 28 N.s, m = 4 Kg, and vi = 3 m/s
vf = (28N.s/4kg) + 3m/s = 7m/s + 3m/s
vf = 10 m/s.
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