# How Do You Calculate The Distance Traveled By An Object Using Vector Kinematics?

• Determine the angle which the bullet is fired relative to the ground. This can be done using a simple mathematical compass. • Determine the initial (starting) velocity of the bullet as soon as it leaves the barrel of the gun. This information can usually be found on the gun’s package or off of the internet. The initial velocity of the projectile varies depending on the gun and bullet used. • With a writing utensil and paper, construct an x-y coordinate system with the origin located at the point at which the bullet leaves the barrel. • Using trigonometry, determine the initial velocity in the x and y direction. This can be done using the sine and cosine functions. For example: if the angle of launch is 30o then the sine of 30o, multiplied by the initial velocity, would be the initial velocity in the y-direction. This can most easily be done using a calculator with the trigonometric functions. (sin(30) * vo) Then repeat this step using the cosine function to determine the initial velo