An open-top railroad car (initially empty and of massM0) rolls with negligible friction along astraight horizontal track and passes under the spout of a sandconveyor, sand is dispensed from the conveyor in a narrow stream ata steady rate ΔM/Δt = C and fallsvertically from an average height h above the floor of therailroad car. The car has initial speed v0 andsand is filling it from time t = 0 to t = T.Express your answers to the following in therms of the givenquantities and g.

(a) Determine the mass M of the car plus the sandthat it catches as a function of time t for 0 t T

(b) Determine the speed v of the car asa function of time t for 0 t T

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