Two 72.0 kg hockey players skating at 5.25 m/s collide and stick together.
If the angle between their initial directions was 125 degrees, what is their speed after the collision?
Apply the law of conservation of linear momentum. Since they both have the same initial momentum magnitude, apply the law along the angle that bisects the velocity vector. That will be their final direction after collision.
2 M Vo cos (125/2) = 2 M *Vfinal
Vfinal = Vo cos 62.5 = 0.4617 Vo = ___
To find the speed of the hockey players after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
(m1*v1 + m2*v2) = (M * V)
Where m1 and m2 are the masses of the hockey players, v1 and v2 are their initial velocities, M is the total mass of the players after the collision, and V is their final velocity.
In this case, m1 = m2 = 72.0 kg (since both players have the same mass), v1 and v2 are the initial velocities of the players (5.25 m/s), and we need to find the final velocity V.
Since the collision makes the players stick together, their final combined mass is M = m1 + m2 = 72.0 kg + 72.0 kg = 144.0 kg.
Now, let's substitute these values into the conservation of momentum equation:
(72.0 kg * 5.25 m/s + 72.0 kg * 5.25 m/s) = (144.0 kg * V)
Simplifying the equation:
(378 kg*m/s + 378 kg*m/s) = (144.0 kg * V)
756 kg*m/s = 144.0 kg * V
Dividing both sides of the equation by 144.0 kg:
756 kg*m/s / 144.0 kg = V
5.25 m/s = V
So the speed of the hockey players after the collision is still 5.25 m/s.
To determine the speed of the two hockey players after the collision, we need to use the principles of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity.
Let's denote the mass of each hockey player as m = 72.0 kg.
The initial momentum before the collision can be calculated as:
Initial momentum = m1 * v1 + m2 * v2,
where m1 and m2 are the masses of the two hockey players and v1 and v2 are their respective velocities.
Let's break down the initial velocities of the two hockey players into their x and y components based on the given angle of 125 degrees:
v1x = v1 * cos(theta1) = 5.25 m/s * cos(125 degrees),
v1y = v1 * sin(theta1) = 5.25 m/s * sin(125 degrees),
v2x = v2 * cos(theta2) = 5.25 m/s * cos(180 degrees - 125 degrees),
v2y = v2 * sin(theta2) = 5.25 m/s * sin(180 degrees - 125 degrees).
Note that for the second player, we use 180 degrees minus the given angle because they are initially moving in the opposite direction.
Now, let's calculate the initial momentum:
Initial momentum = (m1 * v1x + m2 * v2x) î + (m1 * v1y + m2 * v2y) ĵ,
where î and ĵ are the unit vectors in the x and y directions.
Next, we need to determine the final velocity after the collision. Since the hockey players stick together, their mass will be combined, and we can calculate the final velocity using the total mass and momentum.
Let's denote the total mass after the collision as M = 2 * m, where 2 is the number of hockey players.
The final velocity of the combined hockey players can be calculated using the final momentum and the total mass:
Final velocity = Final momentum / M.
Now, let's substitute the values into the equations and calculate the final velocity after the collision.