Alice and Bob are passengers in a high-speed train moving at a uniform speed of v = c/2. Alice is at the rear of the train car and Bob is at the front of the car. The length of the car measured in their frame is L'. Alice throws a ball to Bob at speed u' = c/3.
a) In the frame of the train, how long does it take the ball to reach Bob?
b) In the frame of the station, how long does it take the ball to reach Bob?
c) In the frame of the ball, how long does it take the ball to reach Bob?
d) Verify that the proper time between Alice throwing the ball and Bob receiving it is the same in all three frames.

Independent variable is something that is changed in a experiment. 

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

What kind of enegia produces the mixture of bicarbonate and vinegar  chemical producetion