How can R-27 missiles hit the F-15 ?

Houthis modified it to become SAM, accelerations when firing from the surface would not be as accelerated as the R-27 was launched from high-altitude and high-speed aircraft. The R-27 will not have enough speed, range and well as a flying ceiling to attack F-15s flying at high speed

Can be specific examples AIM7P vs RIM7P

AIM-7P Sparrow Specifications
Dimensions
Diameter: 200 millimeter (7.87 inch)
Length: 3.66 meter (144 inch)
Wingspan: 1.02 meter (40 inch)
Performance
Max Range: 55,000 meter (29.7 nautical mile)
Speed
Top Speed: 1,190 mps (4,285 kph)
Weight
Warhead: 40 kilogram (88 pound)
Weight: 227 kilogram (500 pound)

RIM-7P Sea Sparrow Specifications
Dimensions
Diameter: 200 millimeter (7.87 inch)
Length: 3.66 meter (144 inch)
Wingspan: 1.02 meter (40 inch)
Performance
Max Range: 35,000 meter (18.9 nautical mile)
Speed
Top Speed: 1,190 mps (4,285 kph)
Weight
Warhead: 40 kilogram (88 pound)
Weight: 227 kilogram (500 pound)

http://www.deagel.com/Defensive-Weapons/AIM-7P-Sparrow_a001156002.aspx

https://theaviationist.com/2018/01/09/yemens-shiite-houthis-claim-saudi-f-15-kill-with-sam-over-capital-city-of-sanaa/

For a big acceleration, SAM needs a bigger engine than AAM and SAM size is always bigger than AAM. The Patriot’s rocket motor has a weight of over 600 kg and a thrust of more than 10 tonnes, helps it reach speeds Mach 2.8-4.1

Thiokol TX-486 Single-Thrust Motor

Length: 3.2m
Diameter: 0.41m
Propellant: 1,115 lbs (506 kg) of HTPB-AP, with an ISP of 258.
Thrust: 24,052 lbf (10,910 kgf) for 12 seconds
Weight: 1,400 lbs (635 kg)

http://www.alternatewars.com/BBOW/Weapons/US_SAMs.htm

AAM’s rocket motor is not able to achieve the same thrust and weight as SAM’s rocket motor

For a big acceleration, SAM needs a bigger engine than AAM and SAM size is always bigger than AAM. The Patriot’s rocket motor has a weight of over 600 kg and a thrust of more than 10 tonnes, helps it reach speeds Mach 2.8-4.1 (Patriot missile weighs 900kg)

Thiokol TX-486 Single-Thrust Motor

Length: 3.2m
Diameter: 0.41m
Propellant: 1,115 lbs (506 kg) of HTPB-AP, with an ISP of 258.
Thrust: 24,052 lbf (10,910 kgf) for 12 seconds
Weight: 1,400 lbs (635 kg)

http://www.alternatewars.com/BBOW/Weapons/US_SAMs.htm

The AIM-120 missile rocket motor weighs 75.34 kg. The thrust is certainly not more than 10 tons but it still achieves Mach 4 speed. This is due to the high altitude and high speed launch from aircraft

AAM’s rocket motor is not able to achieve the same thrust and weight as SAM’s rocket motor