Answer:
(a) Height is 4.47 m
(b) Height is 4.37 m
Solution:
As per the question:
Initial velocity of teh ball, 
Angle made by the ramp, 
Distance traveled by the ball on the ramp, d = 5.00 m
Now, 
(a) At any point on the projectile before attaining maximum height, the velocity can be given by the eqn-3 of motion:

where
H =  
 
g = 

 = 19.06 m/s
 = 19.06 m/s
Now, maximum height attained is given by:


Height from the ground = 
(b) now, considering the coefficient of friction bhetween ramp and the ball,  :
:
velocity can be given by the eqn-3 of motion:


 = 18.7 m/s
 = 18.7 m/s
Now, maximum height attained is given by:


Height from the ground = 
 
        
             
        
        
        
F = G Mm/r²
mg = G Mm/r²
g = GM/r²
At centre of earth, r=0
g = GM/0 
g =0
        
                    
             
        
        
        
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Answer is C.
 
        
                    
             
        
        
        
Here in all such collision type question we can use momentum conservation as we can see that there is no external force on this system

as we know that




now from above equation we have



so the speed of combined system is 2 m/s