1. One way that scientists measure the mass of an unknown particle is to bounce a known particle, such as a proton or an

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1. One way that scientists measure the mass of an unknown particle is to bounce a known particle, such as a proton or an electron, off the unknown particle in a bubble chamber. The initial and rebound velocities of the known particle are measured from photographs of the bubbles it creates as it moves; the information is used to determine the mass of the unknown particle.
A. If a known particle of mass 𝑚 and initial speed 𝑣0 collides elastically, head-on with a stationary unknown particle and then rebounds with speed 𝑣, find an expression for the mass 𝑚u of the unknown particle in terms of 𝑚, 𝑣, and 𝑣0.
𝑚u=
B. Assume that the known particle is a proton, with initial speed 𝑣0=3.00×10^4 m/s, and that the unknown particle is a neutron. What will be the recoil speed 𝑣p of the proton?
𝑣p= m/s
C. What will be the final speed 𝑣n of the neutron?
𝑣n= m/s
2. Two hockey players collide on the ice and go down together in a tangled heap. Player 1 has a mass of 105kg and player 2 has a mass of 92.0kg. Before the collision, player 1 had a velocity 𝑣⃗ 1,i of 6.10 m/s6.10 m/s in the +𝑥 direction, and player 2 had a velocity 𝑣⃗ 2,i of 5.60 m/s at an angle 𝜃2,i of 72.0∘ with respect to the +𝑥 -axis, as shown in the figure.
At what final speed 𝑣f do the players slide together on the ice after the collision?
𝑣f= m/s
At what angle 𝜃f relative to the +𝑥-axis do the players slide together on the ice after the collision?
𝜃f=
please answer all