Step-by-step explanation:
Formula that relates the mass of an object at rest and its mass when it is moving at a speed v:

Where :
m = mass of the oebjct in motion
= mass of the object when at rest
v = velocity of a moving object
c = speed of the light = 
We have :
1) Mass of the Dave = 
Velocity of Dave ,v= 90% of speed of light = 0.90c
Mass of the Dave when moving at 90% of the speed of light:

m = 151.41 kg
Mass of Dave when when moving at 90% of the speed of light is 151.41 kg.
2) Velocity of Dave ,v= 99% of speed of light = 0.99c
Mass of the Dave when moving at 99% of the speed of light:

m = 467.86 kg
Mass of Dave when when moving at 99% of the speed of light is 467.86 kg.
3) Velocity of Dave ,v= 99.9% of speed of light = 0.999c
Mass of the Dave when moving at 99.9% of the speed of light:

m = 1,467.17 kg
Mass of Dave when when moving at 99.9% of the speed of light is 1,467.17 kg.
4) Mass of the Dave = 
Velocity of Dave,v=?
Mass of the Dave when moving at v speed of light: 500


Dave should be moving at speed of
.