Derivation of Velocity of the Ballistic Pendulum and Its Lowest Point of Travel
| Tbottom = mgH1 + 1/2 mVbottom2 | Energy is Conserved |
| Ttop = mgH2 + 1/2 m(Vtop)2 | H1 = 0 |
| mgH1 + 1/2 mVbottom2 = mgH2 + 1/2 m(Vtop)2 | Vtop = 0 |
| 1/2 mVbottom2 = mgH | Divide by m; m cancels |
| 1/2 Vbottom2 = gH | multiply both sides by 2 |
| V2 = 2gH | Square root both sides |
| V = sqr. Root(2gH) | H = L(1 - cosq ) |
V = sqr. Root(2gL [1 - cosq ])
Note: Refer to the Derivation of the Change in Height of Ballistic Pendulum to find out
how derive H = L(1 - cosq )