Design a lab Trajectory

Hyun
Kim, Christy, Rin
Physics, Blk 2
Mr. Elwer

Introduction : As human trow a ball, brain automatically calculate the angle and throw in a hyperbolic path so that the ball goes to exact spot. Hyperbolic path of the projectile provides lots of information: launching angle, initial velocity, maximum height of projectile, total displacement when the object first hit the ground. Lots of other information can be derived from these information. Students should be using trigonometric equations and bunch of physics equations to calculate all the measurements. The purpose of this lab was to get the initial velocity of projectile and the angle that is has been thrown with when we were given the length, the angle of the projectile form a observer who is 7m apart from the projectile. From this lab, we would be able to get the angle of the projectile when it was thrown, and initial velocity that ball possesses.

Materials : To compete this lab, we need: Mr. Elwer(as a pitcher), couple cones, tape measure, couple student with angle gun, and balls.

Experimental Design : On this lab angles that students measure and the total displacement of projectile will be crucial because as those independent variables change, dependent variables such as angle of projectile and initial velocity will change. To do this accurately Mr. Elwer and angle observers shouldn't be moving, and someone should measure the distance pretty accurately by putting cones exactly where projectile hit the floor.

Procedures :
     1. Go outside to find enough space
     2. Place Mr. Elwer on a position, angle observers, and a student who will record the displacement
     3. Throw the ball, measure the displacement, and angle of maximum height of the ball.       *make sure thrower do the overhand mother and angles are between 20' to 70'.
     4. Repeat 3 couple times so that we can get the accurate data.


Date Table :

Trial #	Angle (')	Distance (m)
1	32	15.9 m
2	38	14.5 m

1st Trial:

Minimum distance between observer and the path of the projectile = 7m

Height of Thrower and Observer = 2m

Angle of angle gun = 32

Displacement = 15.9

Acceleration from gravity(a) = -9.81

Velocity of Projectile in y direction when it hits the maximum point (Vyf) = 0

Total Height of the Projectile when it hits the maximum point = 2+7*tan(32)

h = h_i + v_it + at²/2

7tan32=(9.81)t^2/2

t=.944331=.94s

Vyf=Vyi+at, 0=Vi+(-9.81)*t

Vyi=9.26388=9.3m/s

Vx=d/t, Vx=15.9/(.944331*2)=8.41866=8.4m/s

use pitagorian theorem Vi=sqroot(Vx^2+Vyi^2)=12.5177=13m/s

angle=arctan(9.3/8.4)=48'

2nd Trial

Total Height of the Projectile when it hits the maximum point = 2+7tan(38)

7tan38=(9.81)t^2/2

t=1.05593=1.1s

0=Vi+(-9.81)*t

Vyi=10.3587=10.m/s

Vx=d/t, Vx=14.5/(1.05593*2)=6.866=6.9m/s

Vi=sqroot(Vx^2+Vyi^2)=12.4275=12m/s

angle=arctan(10/6.9)=56'

Graphs :

Time vs Position

Conclusion : Mr Elwer was throwing the balls with about 50 degrees and with about 12m/s. this tells that we could get the initial velocity of projector and angle from height of the object's maximum height. However, this lab can show me huge error because, as people use the angle gun, there can be huge error. to improve this problem, we can buy a new, fancy, and expensive machine to measure the angle, otherwise, we have to go over the procedure over dozens of times.