Biniam Aran, 27, died from multiple injuries after being struck by the vehicle, which was on its way to arrest a suspected hitman in south London last February.
His stepbrother Amanuel Fasil, who lived with Mr Aran in Meadow Road, Lambeth, south London, told Southwark Coroner's Court that he and a friend managed to leap to the safety of a traffic island.
But Mr Aran, an economics student at East London Polytechnic who was behind them on the crossing, was hit and catapulted across to the other side of Clapham Road.
The Range Rover drove on. Two police vehicles behind did stop and called an ambulance but Mr Aran was certified dead half an hour later in hospital.
Mr Fasil said they were on their way home at about midnight on 26 February after drinking at a pub. He said: 'We were walking quite steadily when the vehicle came from nowhere. We jumped on to the island and as soon as I reached it, I turned to see what had happened and I glimpsed my brother being hit by the car. For a split second, I could see his body flying.'
He said, under questioning from the coroner, Sir Montague Levine, that the vehicle was travelling at between 80 and 100mph.
The Range Rover was one of a convoy of three vehicles on their way from Old Street police station north of the City, going in search of a suspected contract killer in Wimbledon, south-west London.
Sergeant George Grant, who was a front-seat passenger, admitted the Range Rover had been going 'fast' as it turned into Clapham Road but said he was looking at a map as it approached the crossing.
He did not know at what speed it was travelling, although it was slowing down. Blue flashing lights and a two-tone horn on the vehicle were in use.
Sgt Grant said he saw two men in the road but could not say whether they were on the crossing or not. A third man stayed on the pavement but then put one foot on the road before moving back to the pavement.
He said he then saw the third man run across the road - not on the crossing - and collide with the front door of the vehicle.
Inspector Andrew Latto, who was in the rear passenger seat, said the vehicle was 'definitely' going faster than the 30mph speed limit. He heard a bang as it went over the crossing and it took the Range Rover between 75 and 100 yards to pull up.
He strongly denied an allegation by Benedict Birnberg, for Mr Aran's family, that the Range Rover did not stop afterwards.
'We pulled up about 75 to 100 yards beyond the crossing and I got out and went straight back to the body,' he said. The other officers stayed near the vehicle while an ambulance was called.
Constable Carl Bennett, driving a second Range Rover in the convoy, told the inquest his vehicle was travelling at 50 to 60mph as it approached the pedestrian crossing. He said neither vehicle was travelling at 80 to 100mph, as had been suggested.
The inquest continues today.