A bunch of my friends and I are going paintballing after midterms for the first time. Paintballing is like a physics teacher's dream and possibly a physic student 's nightmare. Paintballing is basically all about projectiles. A projectile is an object that is acted upon by only gravity. This describes the paintball after it has left the paintball gun. Now I want to walk away from this outing with as few as bruises as possible. I want to figure out how far away I have to be from my friends in order to avoid being hit by the paint ball gun. This will also be the same distance I have to be in order to hit my friends with paintballs. Because lets face it paintballing isn't paintballing unless you hit someone. The average initial velocity of a paintball as it leaves a paintball gun is about 85m/s. My friends are about five feet and five inches which converts to about 1.65 meters. This is how high the paint ball is from the ground when starting. If I stand about 20 meters away will I get hit? We can start to solve this problem by listing our givens

Horizontal Vertical

vi = 85m/s vi= 0

vf = vf=

d = 20 m d= 1.65 m

a = 0 a= 9.81 m/s²

t= t=

In order to solve this question we need to figure out if the horizontal distance is less than or greater than 20 meters. if it is less than 20 meters than I'll be safe. if it is greater than 20 meters well l wont be safe. We will have to start by solving for vertical time. Because time is the same vertically and horizontally we will then use this same time to solve for d horizontally.

We can use the equation d= vit + 1/2at² in order to solve for t vertically. First we must take notice that vi = 0 so we can simplify the equation to d= 1/2at² Now we can rearrange this equation so that we are solving for t. t= √2d/a When you substitute with units and numbers you find that t= .58 seconds.

Now we use this same equation d=vit + 1/2at² to find d horizontally. This is how far the paintball will land. Take notice that since a=0 we can simplify this equation as well to d= vit when we substitute with numbers and units d= (85m/s)(.58s) we find out that the paint ball will travel 49.3 meters.

Notice this distance is greater than the distance of where I am standing. In conclusion I am in trouble.