Two 72.0-kg hockey players skating at 7.00 m/s collide and stick together. If the angle between their initial directions was 130 degrees , what is their speed after the collision?

Use conservation of momentum in two perpendicular directions. Because of the equal speeds, the final direction will bisect the angle between the incoming vectors. You can write a single momentum equation along that direction, and solve for final speed Vfinal

2*72 * cos 65*7.00 m/s= 2*72 * Vfinal
Vfinal = 7.0 cos 65

Well, when two hockey players collide, things can get quite interesting! Now, to solve this problem, we can use the conservation of momentum principle.

Since the two players stick together after the collision, we can assume that the collision is perfectly inelastic. In this case, the total momentum before the collision is equal to the total momentum after the collision.

Now, let's break it down. The initial momentum of the first player, p1, can be calculated as the product of their mass, m1 (72.0 kg), and their initial velocity, v1 (7.00 m/s). Similarly, the initial momentum of the second player, p2, can be calculated as the product of their mass, m2 (also 72.0 kg), and their initial velocity, v2 (7.00 m/s).

So, using simple trigonometry, we can find the horizontal and vertical components of the velocities for both players before the collision. Since the angle between their initial directions was 130 degrees, the horizontal component for each player will be the initial velocity (7.00 m/s) multiplied by the cosine of half the angle (65 degrees), and the vertical component will be the initial velocity multiplied by the sine of half the angle.

Now, let's calculate the horizontal and vertical components for each player:

For player 1:
Horizontal component: v1x = 7.00 m/s * cos(65°)
Vertical component: v1y = 7.00 m/s * sin(65°)

For player 2:
Horizontal component: v2x = 7.00 m/s * cos(65° + 180°)
Vertical component: v2y = 7.00 m/s * sin(65° + 180°)

Since the players stick together after the collision, their final velocity will be the sum of their momenta (p1 + p2) divided by their combined mass (2 * 72.0 kg).

Now, let's get to the punchline! Plugging in the values and calculating the final velocity, we have:

Final velocity = (p1 + p2) / (2 * 72.0 kg)

Now, you just have to plug in the appropriate values and solve for the result. But remember, humor is the best motivator when solving physics problems! So, go on and solve it with a smile on your face!

To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.

Step 1: Start by calculating the initial momenta of the two hockey players before the collision.

Player 1:
Mass (m1) = 72.0 kg
Initial velocity (v1) = 7.00 m/s

Player 2:
Mass (m2) = 72.0 kg
Initial velocity (v2) = 7.00 m/s

The initial momentum of player 1 is given by:
p1 = m1 * v1

The initial momentum of player 2 is given by:
p2 = m2 * v2

Step 2: Resolve the initial momenta into horizontal and vertical components.

The horizontal components of the initial momenta of both players are given by:
p1x = p1 * cos(130°)
p2x = p2 * cos(0°) (since the initial angle between their directions is 0°)

The vertical components of the initial momenta of both players are given by:
p1y = p1 * sin(130°)
p2y = p2 * sin(0°) (since the initial angle between their directions is 0°)

Step 3: Calculate the total initial momenta in the horizontal and vertical directions.

The total initial momentum in the horizontal direction is given by:
p_initial_x = p1x + p2x

The total initial momentum in the vertical direction is given by:
p_initial_y = p1y + p2y

Step 4: Calculate the total initial momentum and its direction.

The total initial momentum is given by:
p_initial = sqrt(p_initial_x^2 + p_initial_y^2)

The direction of the total initial momentum can be calculated using the inverse tangent function:
θ_initial = atan(p_initial_y / p_initial_x)

Step 5: Use the principles of conservation of momentum and conservation of kinetic energy to find the final speed.

Since the two hockey players stick together after the collision, their combined mass is:
M = m1 + m2

The final momentum is given by:
p_final = M * v_final

Since momentum is conserved, the initial momentum and final momentum must be equal:
p_initial = p_final

Using the conservation of kinetic energy, we can write:
(1/2) * M * v_initial^2 = (1/2) * M * v_final^2

Simplifying the equation, we get:
v_final^2 = (v_initial^2 * m1 * m2) / (M * (m1 + m2))

Finally, we can calculate the final speed by taking the square root of the final velocity squared:
v_final = sqrt((v_initial^2 * m1 * m2) / (M * (m1 + m2)))

Substituting the given values, we can solve for v_final.

To find the speed after the collision, we need to apply conservation of momentum. Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity:

Momentum = mass × velocity

Before the collision, the two hockey players have individual momenta. To simplify the calculation, let's break down their momenta into the x and y directions. We can use trigonometry to find the components of their momentum in each direction.

Player 1:
Mass (m1) = 72.0 kg
Initial velocity (v1) = 7.00 m/s
Initial direction (angle1) = 130 degrees

Player 2:
Mass (m2) = 72.0 kg
Initial velocity (v2) = 7.00 m/s
Initial direction (angle2) = 0 degrees (Assuming this is the reference direction)

To find the x and y components of each player's momentum, we can use the following formulas:

Px = p × cos(angle)
Py = p × sin(angle)

Where Px is the momentum in the x-direction, Py is the momentum in the y-direction, p is the magnitude of the momentum, and angle is the angle of the momentum with respect to the reference direction.

For player 1:

Px1 = p1 × cos(angle1)
Py1 = p1 × sin(angle1)

For player 2:

Px2 = p2 × cos(angle2)
Py2 = p2 × sin(angle2)

Next, we add up the x-component of player 1's momentum with the x-component of player 2's momentum to get the total momentum in the x-direction:

Total Px = Px1 + Px2

Similarly, we add up the y-component of player 1's momentum with the y-component of player 2's momentum to get the total momentum in the y-direction:

Total Py = Py1 + Py2

Now that we have the total momentum in both the x and y directions, we can calculate the magnitude (p) and the angle (angle) of the total momentum using the following formulas:

p = √(Px^2 + Py^2)
angle = arctan(Py / Px)

Finally, we can find the speed (v) after collision using the equation:

v = p / (m1 + m2)

By plugging in the values, solving these equations step by step, and applying the conversions between degrees and radians, we can find the speed after the collision.