Two identical freight sleds, P and Q, coast on a perfectly straight, horizontal guideway with constant speeds. The +x axis points east.
• Sled P travels east with speed vP/E (unknown).
• Sled Q travels west with speed vQ/E (unknown).
Each sled has a roof-mounted conveyor belt that can move cargo along the line of motion.
• A package on sled P moves 1.5 m/s east relative sled P.
• A package on sled Q moves 1.0 m/s east relative sled Q.
A camera fixed to Earth records that, at the instant the two sleds pass each other, the two packages have equal-magnitude speeds relative Earth but travel in opposite directions (one east, the other west). At the same instant, an operator riding on sled P observes the package on sled Q pass by at 22 m/s toward the west.
(1) Write separate expressions for the velocity of each package relative Earth, using clear two-subscript notation.
(2) Use the camera’s observation to derive an equation relating vP/E and vQ/E.
(3) Using both the equation from part (b) and the operator’s observation, determine numerical values for vP/E and vQ/E (include directions).
(4) Briefly discuss whether your results for the sled speeds would change if both conveyor belts were shut off immediately after the instant of observation. Explain your reasoning.