Relativity: Relativistic Kinematics and Dynamics

[fingerprintregion]

Homework Statement

1. Two cannons, a & b, positioned at Xa = 0 km and Xb = 1,5 km, both shoot at an approaching rocket. a shoots at t = 0 and b shoots at t = 1 µs. The rocket’s detector detected both cannons shot at the same time. What is the speed of the rocket?
2. Three light sources, A, B, C emit monochromatic light of frequency f0. Relative to A, B has the speed of +v and C has the speed of -v. Determine the light frequency accepted by C from A and B if
a. B approaches C
b. B recedes C
3. A particle has the energy of 4m0c^2. What is the particle’s momentum? What is the particle’s energy if the momentum = 2m0c?
4. A high-energy proton collides with another proton at rest so that a particle, π^0 is created. Determine the energy needed by the proton to make this happen. Proton mass = u, π^0 mass = 0,1449 u, u = 1.67 x 10^-27 kg.

Relevant Equations

Time dilation, length contraction, relativity

I’ve read Beiser’s Modern Physics Chapter 1 and I am able to grasp the general theories but not so much when applying it to problems. I major in Chemistry and would really appreciate any head start/help/suggestions. For number 1 I thought of using L = L0 sqrt 1-v^2/c^2 but can’t seem to find the use of t. Number 3 I thought of using E = mc^2.

 

[mfb]

Look up relativity of simultaneity.

E=mc² is the energy at rest. You'll need the more general expression linking energy, mass and momentum.