Another go.

Bloodhound state a fully-fueled mass of 7868 kg. They further quote 90 kN thrust for the EJ-200.

Way back in 1687 Newton came up with F=ma. So, from rest, running on jet power only, a fully-fueled 7868 kg Bloodhound will accelerate at not more than a = F/m or 90,000 N / 7868 kg = 11.44 m/s**2, or about 1.17g.

The web site quotes 6227 kg dry with driver. So, if both the rocket and the EJ-200 are running at maximum thrust of 212 kN, just before the fuel runs out (ignoring aero drag!) the acceleration cannot be more than 3.47g.

At peak speed, using the BH SSC tech data (Cda = 1.3, V = 469 m/s), overcoming drag will consume 142 kN. That leaves about 70 kN left over to accelerate the 6227 kg. Again, a = F/m or a = ~11.3 m/s**2 or about 1.15g.

If you look at the mass breakdown, the EJ200 weighs 1200 kg (or 20% of the dry weight). The jet fuel tank, fuel, and intake structure weigh about 550 kg. So if you toss the jet overboard you've reduced your fully-fueled mass by at least 1750 kg, or 22%. If you then substitute a gas pressurization system for the "APU" (and the associated APU cooling system) you might shed a further 360 kg or so, leaving you at 5700 kg rather than 7800+.

Currently, the rocket propellant is specified as about 200 kg and HTP mass is nearly 1000 kg. So add some mass back in to increase the fuel burn beyond 20 seconds... to get it to 40 seconds, presumably you'd double that. So you are back up to 6500 kg or so, assuming some modest reduction elsewhere.

But what do I know? I'm a telecom guy and web forum lurker... but this stuff is cool