This tarantula video has been slowed down to take away doubt a tarantula could propel itself up and forward through the air, meaning a jump.
The best past reviewing the footage in frame by frame, it had a going motion. Due to reaching its prey it stopped, if it were further the jump would have been greater. This from a giant white knee, a heavy terrestrial tarantula.
Here is a P.irminia coiling down and back to jump, look at the distance even some lift and if the platform the persons hand was angled more upwards imagine the height. The video was also slowed down, enjoy.