This is just a blog post for the derivation of solving the initial velocity of a projectile when you are just given the range, angle, and height of the object you are trying to hit.

Let:

R = Range |

V_{0} = Initial Velocity |

θ = Angle |

y = Height |

x = Distance |

**Equation 1 y-component of the projectile
**

**Equation 2 x-component of the projectile
**

Therefore, at *t _{flight}*,

*y*=

*y*and

*x*=

*R*. Using equations 1 and 2 again:

**Equation 3 y-component of the projectile at t_{flight
}**

**Equation 4 x-component of the projectile at t_{flight
}**

To get *V*_{0x} and *V*_{0y}:

**Equation 5
**

**Equation 6
**

Substituting:

**Equation 7
**

**Equation 8
**

Solving for *t _{flight }*from equation 7 and substituting equation 9 to 8:

**Equation 9
**

**Equation 10
**

Simplifying:

**Equation 11 Final Equation**