- #1
Ruddie
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Homework Statement
Hello, I have an issue regarding projectile trajectory.
As an assigment we have made a trebuchet, which is basically a catapult with a sling attached to it.
We have done some measurements with the trebuchet itself, and have actually achievement some (according to us) correct results. The theory however, gave us a strange result.
We decided we wanted to know the velocity of our projectile (which should have been easy..)
Which we determined ourself, and confirmed using wikipedia.
The velocity we received from calculating this ( see 3 ) was approx 277 m/s. Which of course, is impossible since our projectile traveled only 20 meters and did not reach it's destination that fast, what did we do wrong?
We assumed we shot approx. at 45 degrees, making alpha = 45.
The distance traveled was 20 meters, making d = 20.
The g is the gravitational force, since we were testing on our own planet g = 9.81.
y_0 is the height we shot the projectile from, in our case this was 80 cm, making y_0 = 0.80.
Homework Equations
We used this formula:
d = v*cos(alpha)/g * ( v*sin (alpha) + sqrt((v*sin(alpha))^2+2*g*y_0) )
The Attempt at a Solution
Using the above variables.. we calculated the velocity like this:
20 = v*cos(45)/9.81 * ( v*sin ( 45 ) + sqrt((v*sin(45))^2+2*9.81*0.8) )
20 = v*cos(45)*v*sin(45)/9.81 + v*cos(45)sqrt((v*sin(45))^2+2*9.81*0.8)/9.81
Where..
cos(45) = sin(45) = .5sqrt(2)
This gives us:
20 = 0.5*v^2/9.81 + .5*v*sqrt(2)*sqrt(.5*v^2+15,696)/9.81
20^2 = (0.5*v^2/9.81)^2 + (0.5*v*sqrt(2)*sqrt(.5*v^2+15,696)/9.81)^2
400 = .25*v^4/9.81^2 + .5*v^2*(.5*v^2+15.696)/9.81^2
400 = .5*v^4+7.848v^2/9.81^2
.5*v^4 + 7.848*v^2 = 38494.44
v^4+15.696v^2 = 76988.88
v^2(v^2+15.696) = 76988.88
v^2 = 76988.88 OR v^2 + 15.696 = 76988.88
v = 277.47 OR v^2 = 76973.184
v = 277.47 OR v = 277.44Thanks in Advance for checking out my problem.
p.s. I just figured this might have fitted better in the Advanced Physics part?
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