1. Determine the theoretical range of the launcher for the 3 cases specified bel
ID: 1355080 • Letter: 1
Question
1. Determine the theoretical range of the launcher for the 3 cases specified below.
2. Comment on the accuracy of your results to these theoretical values. What might be causing amy of the differences?
0= y0 + v0sin(theta)T-1/2gT2
Horizontal Velocity: vx=v0cos(theta)
Vertical Velocity: vy=v0sin(theta)-gt
Horizontal Position: x(t)=vxt
Vertical Position:y(t)=y0+v0sin(theta)t-1/2gt2
Yo= 96.7 cm (Distance from floor up to end of barrel)
ax = 0
ay = -g = -9.81 m/s2
Trial 1
30, 2nd notch = 54.3 cm
45, 3rd notch = 68.0 cm
60, 4th notch = 87.1cm
Trial 2
30, 2nd notch = 66.7 cm
45, 3rd notch = 73.2 cm
60, 4th notch = 87.2 cm
Trial 3
30, 2nd notch = 55.7 cm
45, 3rd notch = 79.6 cm
60, 4th notch = 85.1cm
Average Distance
30 = 58.9 cm
45 = 73.6 cm
60 = 86.5 cm
Explanation / Answer
time taken to reach ground, let be t.
vertical position =0.967+v0*sin(theta)*t-4.905*t^2
hence 0=0.967+v0*sin(theta)*t-4.905*t^2
==>4.905*t^2-v0*sin(theta)*t=0.967....(1)
horizontal distance=v0*cos(theta)*t
let horizontal distance be denoted by D.
then t=D/(v0*cos(theta))
substituting in equation 1,
4.905*(D^2/v0^2)*sec^2(theta)-v0*tan(theta)*(D/v0)=0.967
==>4.905*(D^2/v0^2)*sec^2(theta)=0.967+D*tan(theta)
==>v0^2=(4.905*D^2*sec^2(theta))/(0.967+D*tan(theta))
so for each trial, we will substitute value of D and theta to find corresponding value v0 and compare with the value obtained with average distance.
for theta=30 degree:
average distance=D=0.589 m
==>v0=1.3175 m/s
trial 1:
D=0.543 m
==>v0=1.2272 m/s
trial 2:
D=0.667 m
v0=1.4669 m/s
trial 3:
D=0.557 m
v0=1.2548 m/s
for theta =45 degrees:
average value:
D=0.736 m
v0=1.7665 m/s
trial 1:
D=0.68 m
v0=1.6596 m/s
trial 2:
D=0.732 m
v0=1.7589 m/s
trial 3:
0.796 m
v0=1.8777 m/s
for theta=60 degrees:
average value:
D=0.865 m
v0=2.44 m/s
trial 1:
D=0.871 m
v0=2.452 m/s
trial 2:
D+0.872 m
v0=2.454 m/s
trial 3:
D=0.851 m
v0=2.4127 m/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.