A particle is given velocity `v_0` at point A as shown in the figure. Find the speed of particle at point `B,C` and `D`

Explanation

`K_A=(1)/(2)mv_0^2`,`U_A=mg(2h)=2mgh`
`K_B=(1)/(2)mv_1^2`,`U_B=mgh`
`K_C=(1)/(2)mv_2^2`,`U_C=-mg(2h)=-2mgh`
`K_D=(1)/(2)mv_3^2`,`U_D=0`
`K_A+U_A=K_B+U_B`
`implies(1)/(2)mv_0^2+2mgh=(1)/(2)mg^2+mgh`
`impliesv_1=sqrt(v_0^2+2gh)`
`=K_C+U_Cimpliesv_2=sqrt(v_0^2+8gh)`
`=K_D+U_Dimpliesv_3=sqrt(v_0^2+4gh)`