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Projectile motion Lab report.

Name:

University, Department:

Course:

Lecturer:

Date:

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Objective

To gain an understanding on the aspects of projectile motion e.g. horizontal height,

maximum range, etc.

Introduction

This lab studies the case of 2D projectile motion. In such a case, horizontal and vertical

motion act independently since there is no acceleration in the x direction and there is a constant

acceleration of g (9.8 m/s) in the y direction. The motion of an object in such case can be

determined by the launch angle of the projectile and the initial velocity. The equations that

describe the motion in the x and y direction are as follows:

X-Direction 𝑎𝑥 = 0

𝑣𝑥 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝑣0 𝑐𝑜𝑠𝜃

X=(𝑣0 𝑐𝑜𝑠𝜃)𝑡

Y-Direction 𝑎𝑦 = −𝑔

𝑣𝑦 = 𝑣0 𝑠𝑖𝑛𝜃 − 𝑔𝑡

Y=(𝑣0 𝑠𝑖𝑛𝜃)𝑡 − 𝑔𝑡 2 /2

We can find equations that calculate various aspects of the projectile by

combining these x and y position equations together in various ways. By

combining the x-position and y-position equations, we obtain an equation for

the trajectory of the object:

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Y=𝑥𝑡𝑎𝑛𝜃 − 𝑔𝑥 2 /2(𝑣0 𝑐𝑜𝑠𝜃)2

By setting y=0 in the y-position equation, we see an equation for the total time

travelled by the projectile:

𝑡 = (2𝑣0 𝑐𝑜𝑠𝜃)/𝑔

We can find the total distance in the x-direction (R) by substituting the time

equation into the x-position equation:

𝑅 = (𝑣𝑜2 𝑠𝑖𝑛2𝜃)/𝑔

And finally we can find the maximum ...