Answer to Question #103286 in Mechanics | Relativity for Sam

Question #103286
Two rollerbladers face each other and stand at rest on a flat parking lot. Tony has a mass of 65kg, and Tim has a mass of 52kg. when the push off against one another, Tim acquires a speed of 0.63 m/s. What is Tony’s speed?
Expert's answer

We can find Tony's speed from the law of conservation of momentum. Let's choose the direction in which Tony moves as a positive and apply the law of conservation of momentum:

"m_{Tony}v_{Tony,i} + m_{Tim}v_{Tim,i} = m_{Tony}v_{Tony,f} - m_{Tim}v_{Tim,f},"

here, "m_{Tony} = 65kg" is the mass of Tony, "m_{Tim} = 52kg" is the mass of Tim, "v_{Tony,i} = 0 \\dfrac{m}{s}" is the initial speed of Tony, "v_{Tim,i} = 0 \\dfrac{m}{s}" is the initial speed of Tim, "v_{Tony,f}" is the final speed of Tony and "v_{Tim,f} = 0.63 \\dfrac{m}{s}" is the final speed of Tim.

From this equation we can find the final speed of Tony:

"m_{Tony}v_{Tony,f} - m_{Tim}v_{Tim,f} = 0,""m_{Tony}v_{Tony,f} = m_{Tim}v_{Tim,f},""v_{Tony,f} = \\dfrac{m_{Tim}v_{Tim,f}}{m_{Tony}} = \\dfrac{52kg \\cdot 0.63 \\dfrac{m}{s}}{65kg} = 0.504 \\dfrac{m}{s}."


"v_{Tony,f} = 0.504 \\dfrac{m}{s}."

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