# Projectile Motion Question Thanks!!!?

Projectile motion to date has been seen as how far something will travel at a given initial trajectory and velocity. The practical application of this is slightly different: few want to know about how far something will go. Rather, most applications involve targetting an object at some distance, given a particular initial velocity.

Question - Generate the well-formed, generic solution for determining angle from distance and initial velocity.

THANKS

Relevance

absolute zero.

• Anonymous

The appropriate formula to describe the change in position in the x direction is

Δx = v0_x*t + (1/2)gt^2

The acceleration acting on the x direction is 0,so

xf = v0_x*t

Converting this into polar coordinates you get

xf = (v0cos(Θ)t)

The time it takes for an object in a symmetrical trajectory to hit the ground can be determined from this equation: Δy = v0_y*t + (1/2)gt^2. Set it equal to 0 because you want to find the time it takes when it hits flat on the ground

0 = v0sin(Θ)t - (1/2)gt^2

gt^2 = 2v0sin(Θ)t

t =2 v0sin(Θ)/g

The distance it takes for an object to reach the other end of the trajectory is therefore

v0^2 sin(2Θ)/g = h

Solving for angle it is (1/2)arcsin(gh/v0^2)