How Far Did Big Bertha's Shell Travel?

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AI Thread Summary
The discussion focuses on calculating the distance traveled and time of flight for a shell fired from Big Bertha during World War 1. The initial speed of the shell is given as 2.26 km/s with an inclination of 65.8 degrees. The user is struggling to find the correct time of flight, having obtained multiple incorrect values, including 4.10 s, 0.420 s, and 0.840 s. Clarification is sought on which equations to use and the proper substitutions for calculating time. Accurate calculations are essential to determine the shell's distance traveled in kilometers.
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Homework Statement


During World War 1, the Germans had a gun called Big Bertha that was used to shell Paris. The shell had an initial speed of 2.26 km/s at an initial inclination of 65.8 degrees to the horizontal. The acceleration of gravity is 9.8 m/s^2. How far away did the shell hit? Answer in units of km.
How long was it in the air? Answer in units of s.


Homework Equations


Vf= Vi + a (tf-ti)
y= yi + vit + 1/2 at^2.


The Attempt at a Solution


I did it several different ways and keep getting answers that are wrong. I got 4.10 s for time, then I got .420s and .840 s. I keep getting the wrong answer. Once I figure out how to do time, I'll be able to do the distance part. Keep in mind the a is in meters per second but kilometers is required in the answer.
 
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Which of the two eqns did you use to find the time of flight t? What values did substitute?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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