I.
Introduction
The horizontal distance traveled by a projectile with velocity(v) at an angle( θ ) above the horizontal is known as the range.(Weisstein) Range is dependent on the initial velocity of the projectile, the force of gravity, amount of time spent in motion, and the angle at which it is
2
launched. The equation used to calculate is as follows: Range = 2*V o g*sin2Θ . It is derived from the following kinematic equations:
ΔY = 12 * g * (Δt)2 + V OY * (Δt)
ΔX = V OX * Δt
In these kinematic equations, ΔY equals vertical displacement, g equals the force of gravity on
Earth, Δt is change in time from start to finish, V OY equals initial velocity in the vertical direction, ΔX equals horizontal displacement, and V OX equals the initial velocity in the horizontal direction. To calculate the muzzle velocity of the projectile launcher, the following equations can be used for the x direction and the y direction, respectively. V OX = ||||V O|||| * cosθ , and V OY = ||||V O|||| * sinθ
Objectives:
The purpose of this experiment is to find how the range of a projectile varies with angle.
Hypothesis:
If the above equations defining projectile motion are correct, then the angle of maximum range is 45 o .
List of Equipment:
Launcher and plastic ball
Muzzle loader
Plum bob
Meter sticks (3)
Graph paper
Procedure:
1. Lay three meter sticks in a straight line end to end starting from the edge of the launcher. 2. Fire one shot with the launcher at 10o to approximate where the ball will land. Mark this spot with a pen.
3. Fire five shots and record the distance from the base of the launcher to the spot where the ball lands.
4. Repeat steps 13, increasing the angle of the launcher 10o each time, until reaching
80o .
Include 45o .
Diagram:
Figure 3.1 Shooting on a level surface
9 September 2013
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