Here we can use energy conservation because there is no friction in this setup
now we can say
[tex]KE_i + PE_i = KE_f + PE_f[/tex]
here we will have
[tex]v_i = 3 m/s[/tex]
[tex]PE_i = 0[/tex]
at the maximum height position its speed will become ZERO
So we can say
[tex]KE_f = 0[/tex]
now from above equation
[tex]\frac{1}{2}m(3)^2 + 0 = m(9.81)(h) + 0[/tex]
now we have
[tex]4.5 = 9.81 h[/tex]
[tex]h = 0.46 m[/tex]
