Two stones are thrown vertically upwards simultaneously with their initial velocities u and u respectively. Prove that the heights reached by them would be in the ratio of : (Assume upward acceleration is –g and downward acceleration to be +g).


We know for upward motion,

v2= u2 - 2gh


so,


h=v2 -u2/2g


Highest point v=0


so,


H=u2/2g


Height for first ball, h1= u12/2g


Height for second ball, h2= u22/2g


Then, h1/h2= (u12/2g) /(u22/2g)


= u12/u22


= h1:h2


=u12: u22 Proved


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