Jaymin Abdulrahman, 25, has denied attempted murder, causing grievous bodily harm with intent, and inflicting grievous bodily harm.
It is alleged that the baby was placed into the fifth floor chute at about 6.30pm on September 11 and was found, apparently lifeless, by her father later the same day.Pieces of a broken Moses basket were found in a bin at the bottom of the chute, the court heard.
Abdulrahman told her husband their daughter had been kidnapped by two people and he called the police to report a child snatching, the prosecution told the court.
The baby was taken to Birmingham Children's Hospital with a fractured skull and bleeding on the brain.
She has since been discharged from hospital and is now being cared for by foster parents.
Prosecutors said they believe Abdulrahman knew what she was doing and intended to kill her baby. The court will hear from two psychiatrists about her mental state during the trial.
In his opening speech Mr Andrew Smith QC, prosecuting, told the jury: "Experiments show a dummy of the same size and proportion of the child would have reached maximum speeds of 29mph.
"The drop from the fifth floor would have taken 2.2 seconds before the child would have hit a metal plate designed to deflect rubbish into a bin."
He continued: "It is the prosecution's argument that Jaymin Abdulrahman placed her daughter down the chute through a deliberate act and choice of hers. It was her intention to kill her daughter."
At the conclusion of his opening speech, Mr Smith said: 'The reason why she decided to place her daughter in the rubbish chute may be never be known or understood.
'However, the prosecution say that her intention can be clearly identified from her actions on that September afternoon last year."
The trial continues.