Two 75 kg hockey players skating at 5.50 m per s collide and stick together. if the angle between their initial directions was 120 degress, what is their velocity after the collision?

To solve this problem, we need to use the conservation of momentum.

Step 1: Calculate the initial momentum before the collision.

The momentum of an object is given by the equation: momentum = mass x velocity.

Let's denote player 1 as P1 and player 2 as P2.

P1's initial momentum = mass of P1 x velocity of P1 = 75 kg x 5.5 m/s
P2's initial momentum = mass of P2 x velocity of P2 = 75 kg x 5.5 m/s

Step 2: Calculate the horizontal and vertical components of the momentum.

Since the angle between their initial directions is 120 degrees, we need to find the horizontal and vertical components of the momentum.

Horizontal component of the initial momentum = initial momentum x cos(angle)
Vertical component of the initial momentum = initial momentum x sin(angle)

For player 1:
Horizontal component = (75 kg x 5.5 m/s) x cos(120 degrees)
Vertical component = (75 kg x 5.5 m/s) x sin(120 degrees)

And for player 2:
Horizontal component = (75 kg x 5.5 m/s) x cos(120 degrees)
Vertical component = (75 kg x 5.5 m/s) x sin(120 degrees)

Step 3: Calculate the total horizontal and vertical momentum before the collision.

Total horizontal momentum before the collision = Sum of the horizontal components of P1 and P2

Total vertical momentum before the collision = Sum of the vertical components of P1 and P2

Step 4: Calculate the total momentum before the collision.

Total momentum before the collision = square root[(Total horizontal momentum before the collision)^2 + (Total vertical momentum before the collision)^2]

Step 5: Calculate the total mass after the collision.

Since P1 and P2 stick together after the collision, their total mass is equal to the sum of their individual masses, i.e., 75 kg + 75 kg = 150 kg.

Step 6: Calculate the final velocity after the collision.

The final velocity after the collision is given by: final velocity = total momentum before the collision / total mass after the collision

Plug in the values obtained from previous steps to calculate the final velocity after the collision.

To determine the velocity of the hockey players after the collision, we need to use the principles of momentum conservation. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Step 1: Calculate the initial momenta of the two players
The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the initial momenta of the two hockey players using the following formula:

momentum = mass × velocity

Player 1:
momentum₁ = mass₁ × velocity₁

Given:
mass₁ = 75 kg
velocity₁ = 5.50 m/s

Player 1's momentum = 75 kg × 5.50 m/s = 412.5 kg·m/s

Player 2:
momentum₂ = mass₂ × velocity₂

Given:
mass₂ = 75 kg (since both players have the same mass)
velocity₂ = 5.50 m/s

Player 2's momentum = 75 kg × 5.50 m/s = 412.5 kg·m/s

Step 2: Calculate the total initial momentum
The total initial momentum before the collision is the vector sum of the momenta of the two players. Since the initial angle between their directions is given as 120 degrees, we need to consider this angle when calculating the vector sum.

total initial momentum = √(momentum₁^2 + momentum₂^2 + 2 × momentum₁ × momentum₂ × cos(angle))

Given:
momentum₁ = 412.5 kg·m/s
momentum₂ = 412.5 kg·m/s
angle = 120 degrees

total initial momentum = √((412.5)^2 + (412.5)^2 + 2 × 412.5 × 412.5 × cos(120 degrees))

Step 3: Calculate the final velocity
Since the two players stick together after the collision, they can be treated as a single system. The total final momentum of the system is equal to the total initial momentum.

Therefore, the final velocity of the hockey players after the collision can be found using the following formula:

total final momentum = mass_total_system × velocity_final_system

Given:
mass_total_system = mass₁ + mass₂ = 75 kg + 75 kg = 150 kg

velocity_final_system = total initial momentum / mass_total_system

Now, substitute the value of the total initial momentum calculated in step 2 and solve for velocity_final_system.

velocity_final_system = total initial momentum / mass_total_system

The direction is 120 degrees from each of them.

momentum in that direction only..

cos60*75*5.5*2

velocity= above divided by 150=5.5cos60