Find the equation for the range of a projectile and plug in the numbers.
d = [v²·sin(2θ)] / g = 0.1m
It's a pretty straight-forward equation to derive.
1) Find the hang time of the ball. Do this by looking at the y-components only.
*What you know: v0,y (=v0·sinθ), v,y (=-v0·sinθ), a (=-g)
*What you want to know: t
*Use this equation: a = (v - v0) / t ──► t = (v - v0) / a
t = (-v0·sinθ - v0·sinθ) / -g
= 2v0·sinθ / g
2) Find the horizontal distance traveled. This is a simple v=d/t problem, because the horizontal velocity is constant.
v,x = d / t ──► d = v,x·t = (v0·cosθ)·t
d = (v0·cosθ)(2v0·sinθ / g
= (v0²/g)(2sinθ·cosθ)
The term in the second set of parentheses is a trigonometric identity: sin(2θ) = 2sinθ·cosθ
And so:
d = (v0²/g)sin(2θ)
