In Two Dimensional Motion: Projectile

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.


R = Range
V0 = Initial Velocity
θ = Angle
y = Height
x = Distance


Equation 1 y-component of the projectile

Equation 2 x-component of the projectile

Therefore, at tflight, y = y and x = R. Using equations 1 and 2 again:

Equation 3 y-component of the projectile at tflight

Equation 4 x-component of the projectile at tflight

To get V0x and V0y:

Equation 5

Equation 6


Equation 7

Equation 8

Solving for tflight from equation 7 and substituting equation 9 to 8:

Equation 9

Equation 10


Equation 11 Final Equation