Two 75.0-kg hockey players skating at 5.25 m/s collide and stick together. If the angle between their initial directions was 140 degrees, what is their speed after the collision? (Let the motion of player 1 be in the positive x-direction and the motion of player 2 be at an angle of 140 degrees measured counterclockwise from the positive x-axis.
So I've got the mass(1) and mass(2) = 75 kg. and velocity (1) and velocity (2) = 5.25 m/s. They stick together, so it's inelastic collision.
I used the equation m(1)v(1) + m(2)v(2) = (m(1)+m(2))v(final).
The then solved for the x and y components of v(final) at the angle of 70 degrees. But came up with the wrong answers for each one.
What did I do wrong? I honestly don't know what I did wrong. Please help me!
you cant use that equation. THe equation is a vector equation, and you added them as scalars.
Redo it in each of two directions, perpendicular to each other.
It seems like you're on the right track with using the principle of conservation of momentum in an inelastic collision. However, there might be a mistake in how you calculated the x and y components of the final velocity.
To solve this problem correctly, let's break it down step by step:
1. Start by calculating the initial momentum in the x and y directions for each player. Since player 1 moves in the positive x-direction, its initial momentum in the x-direction would be m₁v₁ cosθ, where θ is the angle between their initial directions (140 degrees in this case). The momentum in the y-direction for player 1 is m₁v₁ sinθ.
2. Similarly, for player 2, the initial momentum in the x-direction would be m₂v₂ cos(180 degrees - θ) = -m₂v₂ cosθ (since it's measured counterclockwise from the positive x-axis), and the momentum in the y-direction would be m₂v₂ sin(180 degrees - θ) = m₂v₂ sinθ.
3. Now, use the equation for conservation of momentum in the x-direction: m₁v₁ cosθ - m₂v₂ cosθ = (m₁ + m₂)v(final) cosφ, where φ is the angle of the final velocity measured counterclockwise from the positive x-axis.
4. Similarly, use the equation for conservation of momentum in the y-direction: m₁v₁ sinθ + m₂v₂ sinθ = (m₁ + m₂)v(final) sinφ.
5. Now, you have two equations with two unknowns (v(final) and φ). You can solve these equations simultaneously to find the values for the final velocity and angle after the collision.
Make sure to check your calculations and apply the correct trigonometric functions (e.g., sin and cos) when finding the x and y components of vectors. Also, be mindful of the signs, especially for vectors in the y-direction.
I hope this helps clarify the approach. Let me know if you have any further questions!